unknown Initial ITS Start location: l4 Program variables: a^0 x^0 y^0 z^0 0: l0 -> l1 : a^0'=a^post1, x^0'=x^post1, y^0'=y^post1, z^0'=z^post1, (1-x^0+x^post1 == 0 /\ 1-x^0 <= 0 /\ a^0-a^post1 == 0 /\ -z^post1+z^0 == 0 /\ -y^post1+y^0 == 0), cost: 1 2: l0 -> l2 : a^0'=a^post3, x^0'=x^post3, y^0'=y^post3, z^0'=z^post3, (1-x^0 <= 0 /\ -a^0-z^0+z^post3 == 0 /\ x^post3-x^0-y^0 == 0 /\ 1+a^post3-a^0 == 0 /\ -z^0+y^post3-y^0 == 0), cost: 1 1: l1 -> l0 : a^0'=a^post2, x^0'=x^post2, y^0'=y^post2, z^0'=z^post2, (z^0-z^post2 == 0 /\ -x^post2+x^0 == 0 /\ -y^post2+y^0 == 0 /\ a^0-a^post2 == 0), cost: 1 3: l2 -> l0 : a^0'=a^post4, x^0'=x^post4, y^0'=y^post4, z^0'=z^post4, (-x^post4+x^0 == 0 /\ -y^post4+y^0 == 0 /\ -a^post4+a^0 == 0 /\ -z^post4+z^0 == 0), cost: 1 4: l3 -> l0 : a^0'=a^post5, x^0'=x^post5, y^0'=y^post5, z^0'=z^post5, (a^0-a^post5 == 0 /\ x^0-x^post5 == 0 /\ -y^post5+y^0 == 0 /\ -z^post5+z^0 == 0), cost: 1 5: l4 -> l3 : a^0'=a^post6, x^0'=x^post6, y^0'=y^post6, z^0'=z^post6, (a^0-a^post6 == 0 /\ x^0-x^post6 == 0 /\ z^0-z^post6 == 0 /\ -y^post6+y^0 == 0), cost: 1 Chained Linear Paths Start location: l4 Program variables: a^0 x^0 y^0 z^0 7: l0 -> l0 : a^0'=a^post2, x^0'=x^post2, y^0'=y^post2, z^0'=z^post2, (1-x^0+x^post1 == 0 /\ a^post1-a^post2 == 0 /\ 1-x^0 <= 0 /\ z^post1-z^post2 == 0 /\ a^0-a^post1 == 0 /\ -z^post1+z^0 == 0 /\ -y^post1+y^0 == 0 /\ -x^post2+x^post1 == 0 /\ y^post1-y^post2 == 0), cost: 1 8: l0 -> l0 : a^0'=a^post4, x^0'=x^post4, y^0'=y^post4, z^0'=z^post4, (-z^post4+z^post3 == 0 /\ x^post3-x^post4 == 0 /\ y^post3-y^post4 == 0 /\ 1-x^0 <= 0 /\ -a^0-z^0+z^post3 == 0 /\ x^post3-x^0-y^0 == 0 /\ 1+a^post3-a^0 == 0 /\ a^post3-a^post4 == 0 /\ -z^0+y^post3-y^0 == 0), cost: 1 6: l4 -> l0 : a^0'=a^post5, x^0'=x^post5, y^0'=y^post5, z^0'=z^post5, (a^0-a^post6 == 0 /\ -y^post5+y^post6 == 0 /\ x^0-x^post6 == 0 /\ z^0-z^post6 == 0 /\ -a^post5+a^post6 == 0 /\ -x^post5+x^post6 == 0 /\ -z^post5+z^post6 == 0 /\ -y^post6+y^0 == 0), cost: 1 Eliminating location l3 by chaining: Applied chaining First rule: l4 -> l3 : a^0'=a^post6, x^0'=x^post6, y^0'=y^post6, z^0'=z^post6, (a^0-a^post6 == 0 /\ x^0-x^post6 == 0 /\ z^0-z^post6 == 0 /\ -y^post6+y^0 == 0), cost: 1 Second rule: l3 -> l0 : a^0'=a^post5, x^0'=x^post5, y^0'=y^post5, z^0'=z^post5, (a^0-a^post5 == 0 /\ x^0-x^post5 == 0 /\ -y^post5+y^0 == 0 /\ -z^post5+z^0 == 0), cost: 1 New rule: l4 -> l0 : a^0'=a^post5, x^0'=x^post5, y^0'=y^post5, z^0'=z^post5, (a^0-a^post6 == 0 /\ -y^post5+y^post6 == 0 /\ x^0-x^post6 == 0 /\ z^0-z^post6 == 0 /\ -a^post5+a^post6 == 0 /\ -x^post5+x^post6 == 0 /\ -z^post5+z^post6 == 0 /\ -y^post6+y^0 == 0), cost: 1 Applied deletion Removed the following rules: 4 5 Eliminating location l1 by chaining: Applied chaining First rule: l0 -> l1 : a^0'=a^post1, x^0'=x^post1, y^0'=y^post1, z^0'=z^post1, (1-x^0+x^post1 == 0 /\ 1-x^0 <= 0 /\ a^0-a^post1 == 0 /\ -z^post1+z^0 == 0 /\ -y^post1+y^0 == 0), cost: 1 Second rule: l1 -> l0 : a^0'=a^post2, x^0'=x^post2, y^0'=y^post2, z^0'=z^post2, (z^0-z^post2 == 0 /\ -x^post2+x^0 == 0 /\ -y^post2+y^0 == 0 /\ a^0-a^post2 == 0), cost: 1 New rule: l0 -> l0 : a^0'=a^post2, x^0'=x^post2, y^0'=y^post2, z^0'=z^post2, (1-x^0+x^post1 == 0 /\ a^post1-a^post2 == 0 /\ 1-x^0 <= 0 /\ z^post1-z^post2 == 0 /\ a^0-a^post1 == 0 /\ -z^post1+z^0 == 0 /\ -y^post1+y^0 == 0 /\ -x^post2+x^post1 == 0 /\ y^post1-y^post2 == 0), cost: 1 Applied deletion Removed the following rules: 0 1 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : a^0'=a^post3, x^0'=x^post3, y^0'=y^post3, z^0'=z^post3, (1-x^0 <= 0 /\ -a^0-z^0+z^post3 == 0 /\ x^post3-x^0-y^0 == 0 /\ 1+a^post3-a^0 == 0 /\ -z^0+y^post3-y^0 == 0), cost: 1 Second rule: l2 -> l0 : a^0'=a^post4, x^0'=x^post4, y^0'=y^post4, z^0'=z^post4, (-x^post4+x^0 == 0 /\ -y^post4+y^0 == 0 /\ -a^post4+a^0 == 0 /\ -z^post4+z^0 == 0), cost: 1 New rule: l0 -> l0 : a^0'=a^post4, x^0'=x^post4, y^0'=y^post4, z^0'=z^post4, (-z^post4+z^post3 == 0 /\ x^post3-x^post4 == 0 /\ y^post3-y^post4 == 0 /\ 1-x^0 <= 0 /\ -a^0-z^0+z^post3 == 0 /\ x^post3-x^0-y^0 == 0 /\ 1+a^post3-a^0 == 0 /\ a^post3-a^post4 == 0 /\ -z^0+y^post3-y^0 == 0), cost: 1 Applied deletion Removed the following rules: 2 3 Simplified Transitions Start location: l4 Program variables: a^0 x^0 y^0 z^0 10: l0 -> l0 : x^0'=-1+x^0, 1-x^0 <= 0, cost: 1 11: l0 -> l0 : a^0'=-1+a^0, x^0'=x^0+y^0, y^0'=z^0+y^0, z^0'=a^0+z^0, 1-x^0 <= 0, cost: 1 9: l4 -> l0 : T, cost: 1 Propagated Equalities Original rule: l4 -> l0 : a^0'=a^post5, x^0'=x^post5, y^0'=y^post5, z^0'=z^post5, (a^0-a^post6 == 0 /\ -y^post5+y^post6 == 0 /\ x^0-x^post6 == 0 /\ z^0-z^post6 == 0 /\ -a^post5+a^post6 == 0 /\ -x^post5+x^post6 == 0 /\ -z^post5+z^post6 == 0 /\ -y^post6+y^0 == 0), cost: 1 New rule: l4 -> l0 : a^0'=a^post6, x^0'=x^post6, y^0'=y^post6, z^0'=z^post6, (0 == 0 /\ a^0-a^post6 == 0 /\ x^0-x^post6 == 0 /\ z^0-z^post6 == 0 /\ -y^post6+y^0 == 0), cost: 1 propagated equality y^post5 = y^post6 propagated equality a^post5 = a^post6 propagated equality x^post5 = x^post6 propagated equality z^post5 = z^post6 Propagated Equalities Original rule: l4 -> l0 : a^0'=a^post6, x^0'=x^post6, y^0'=y^post6, z^0'=z^post6, (0 == 0 /\ a^0-a^post6 == 0 /\ x^0-x^post6 == 0 /\ z^0-z^post6 == 0 /\ -y^post6+y^0 == 0), cost: 1 New rule: l4 -> l0 : a^0'=a^0, x^0'=x^0, y^0'=y^0, z^0'=z^0, 0 == 0, cost: 1 propagated equality a^post6 = a^0 propagated equality x^post6 = x^0 propagated equality z^post6 = z^0 propagated equality y^post6 = y^0 Simplified Guard Original rule: l4 -> l0 : a^0'=a^0, x^0'=x^0, y^0'=y^0, z^0'=z^0, 0 == 0, cost: 1 New rule: l4 -> l0 : a^0'=a^0, x^0'=x^0, y^0'=y^0, z^0'=z^0, T, cost: 1 Removed Trivial Updates Original rule: l4 -> l0 : a^0'=a^0, x^0'=x^0, y^0'=y^0, z^0'=z^0, T, cost: 1 New rule: l4 -> l0 : T, cost: 1 Propagated Equalities Original rule: l0 -> l0 : a^0'=a^post2, x^0'=x^post2, y^0'=y^post2, z^0'=z^post2, (1-x^0+x^post1 == 0 /\ a^post1-a^post2 == 0 /\ 1-x^0 <= 0 /\ z^post1-z^post2 == 0 /\ a^0-a^post1 == 0 /\ -z^post1+z^0 == 0 /\ -y^post1+y^0 == 0 /\ -x^post2+x^post1 == 0 /\ y^post1-y^post2 == 0), cost: 1 New rule: l0 -> l0 : a^0'=a^post1, x^0'=x^post1, y^0'=y^post1, z^0'=z^post1, (0 == 0 /\ 1-x^0+x^post1 == 0 /\ 1-x^0 <= 0 /\ a^0-a^post1 == 0 /\ -z^post1+z^0 == 0 /\ -y^post1+y^0 == 0), cost: 1 propagated equality a^post2 = a^post1 propagated equality z^post2 = z^post1 propagated equality x^post2 = x^post1 propagated equality y^post2 = y^post1 Propagated Equalities Original rule: l0 -> l0 : a^0'=a^post1, x^0'=x^post1, y^0'=y^post1, z^0'=z^post1, (0 == 0 /\ 1-x^0+x^post1 == 0 /\ 1-x^0 <= 0 /\ a^0-a^post1 == 0 /\ -z^post1+z^0 == 0 /\ -y^post1+y^0 == 0), cost: 1 New rule: l0 -> l0 : a^0'=a^0, x^0'=-1+x^0, y^0'=y^0, z^0'=z^0, (0 == 0 /\ 1-x^0 <= 0), cost: 1 propagated equality x^post1 = -1+x^0 propagated equality a^post1 = a^0 propagated equality z^post1 = z^0 propagated equality y^post1 = y^0 Simplified Guard Original rule: l0 -> l0 : a^0'=a^0, x^0'=-1+x^0, y^0'=y^0, z^0'=z^0, (0 == 0 /\ 1-x^0 <= 0), cost: 1 New rule: l0 -> l0 : a^0'=a^0, x^0'=-1+x^0, y^0'=y^0, z^0'=z^0, 1-x^0 <= 0, cost: 1 Removed Trivial Updates Original rule: l0 -> l0 : a^0'=a^0, x^0'=-1+x^0, y^0'=y^0, z^0'=z^0, 1-x^0 <= 0, cost: 1 New rule: l0 -> l0 : x^0'=-1+x^0, 1-x^0 <= 0, cost: 1 Propagated Equalities Original rule: l0 -> l0 : a^0'=a^post4, x^0'=x^post4, y^0'=y^post4, z^0'=z^post4, (-z^post4+z^post3 == 0 /\ x^post3-x^post4 == 0 /\ y^post3-y^post4 == 0 /\ 1-x^0 <= 0 /\ -a^0-z^0+z^post3 == 0 /\ x^post3-x^0-y^0 == 0 /\ 1+a^post3-a^0 == 0 /\ a^post3-a^post4 == 0 /\ -z^0+y^post3-y^0 == 0), cost: 1 New rule: l0 -> l0 : a^0'=a^post3, x^0'=x^post3, y^0'=y^post3, z^0'=z^post3, (0 == 0 /\ 1-x^0 <= 0 /\ -a^0-z^0+z^post3 == 0 /\ x^post3-x^0-y^0 == 0 /\ 1+a^post3-a^0 == 0 /\ -z^0+y^post3-y^0 == 0), cost: 1 propagated equality z^post4 = z^post3 propagated equality x^post4 = x^post3 propagated equality y^post4 = y^post3 propagated equality a^post4 = a^post3 Propagated Equalities Original rule: l0 -> l0 : a^0'=a^post3, x^0'=x^post3, y^0'=y^post3, z^0'=z^post3, (0 == 0 /\ 1-x^0 <= 0 /\ -a^0-z^0+z^post3 == 0 /\ x^post3-x^0-y^0 == 0 /\ 1+a^post3-a^0 == 0 /\ -z^0+y^post3-y^0 == 0), cost: 1 New rule: l0 -> l0 : a^0'=-1+a^0, x^0'=x^0+y^0, y^0'=z^0+y^0, z^0'=a^0+z^0, (0 == 0 /\ 1-x^0 <= 0), cost: 1 propagated equality z^post3 = a^0+z^0 propagated equality x^post3 = x^0+y^0 propagated equality a^post3 = -1+a^0 propagated equality y^post3 = z^0+y^0 Simplified Guard Original rule: l0 -> l0 : a^0'=-1+a^0, x^0'=x^0+y^0, y^0'=z^0+y^0, z^0'=a^0+z^0, (0 == 0 /\ 1-x^0 <= 0), cost: 1 New rule: l0 -> l0 : a^0'=-1+a^0, x^0'=x^0+y^0, y^0'=z^0+y^0, z^0'=a^0+z^0, 1-x^0 <= 0, cost: 1 Step with 9 Trace 9[T] Blocked [{}, {}] Step with 10 Trace 9[T], 10[(1-x^0 <= 0)] Blocked [{}, {}, {}] Accelerate Start location: l4 Program variables: a^0 x^0 y^0 z^0 10: l0 -> l0 : x^0'=-1+x^0, 1-x^0 <= 0, cost: 1 11: l0 -> l0 : a^0'=-1+a^0, x^0'=x^0+y^0, y^0'=z^0+y^0, z^0'=a^0+z^0, 1-x^0 <= 0, cost: 1 12: l0 -> l0 : x^0'=-n+x^0, (-1+n >= 0 /\ -n+x^0 >= 0), cost: 1 9: l4 -> l0 : T, cost: 1 Loop Acceleration Original rule: l0 -> l0 : x^0'=-1+x^0, (1-x^0 <= 0), cost: 1 New rule: l0 -> l0 : x^0'=-n+x^0, (-1+n >= 0 /\ -n+x^0 >= 0), cost: 1 -1+x^0 >= 0 [0]: montonic decrease yields -n+x^0 >= 0 -1+x^0 >= 0 [1]: eventual increase yields (1 <= 0 /\ -1+x^0 >= 0) Replacement map: {-1+x^0 >= 0 -> -n+x^0 >= 0} Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)] Blocked [{}, {}, {10[T], 12[T]}] Step with 11 Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {}, {10[T], 12[T]}, {}] Acceleration Failed marked recursive suffix as redundant Acceleration Failed marked recursive suffix as redundant Step with 11 Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {}, {10[T], 12[T]}, {}, {}] Covered Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {}, {10[T], 12[T]}, {11[T]}] Step with 12 Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)] Blocked [{}, {}, {10[T], 12[T]}, {11[T]}, {12[T]}] Acceleration Failed marked recursive suffix as redundant Acceleration Failed marked recursive suffix as redundant Step with 10 Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 10[(1-x^0 <= 0)] Blocked [{}, {}, {10[T], 12[T]}, {11[T]}, {12[T]}, {}] Covered Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)] Blocked [{}, {}, {10[T], 12[T]}, {11[T]}, {10[T], 12[T]}] Step with 11 Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {}, {10[T], 12[T]}, {11[T]}, {10[T], 12[T]}, {}] Acceleration Failed marked recursive suffix as redundant Covered Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)] Blocked [{}, {}, {10[T], 12[T]}, {11[T]}, {10[T], 11[T], 12[T]}] Backtrack Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {}, {10[T], 12[T]}, {11[T], 12[T]}] Step with 10 Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)], 10[(1-x^0 <= 0)] Blocked [{}, {}, {10[T], 12[T]}, {11[T], 12[T]}, {}] Covered Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {}, {10[T], 12[T]}, {10[T], 11[T], 12[T]}] Backtrack Trace 9[T], 12[(-1+n >= 0 /\ -n+x^0 >= 0)] Blocked [{}, {}, {10[T], 11[T], 12[T]}] Backtrack Trace 9[T] Blocked [{}, {12[T]}] Step with 10 Trace 9[T], 10[(1-x^0 <= 0)] Blocked [{}, {12[T]}, {}] Covered Trace 9[T] Blocked [{}, {10[T], 12[T]}] Step with 11 Trace 9[T], 11[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {}] Step with 11 Trace 9[T], 11[(1-x^0 <= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {}, {}] Covered Trace 9[T], 11[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}] Step with 12 Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {12[T]}] Step with 10 Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 10[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {12[T]}, {}] Covered Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {10[T], 12[T]}] Step with 11 Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {10[T], 12[T]}, {}] Step with 11 Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {10[T], 12[T]}, {}, {}] Covered Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {10[T], 12[T]}, {11[T]}] Step with 12 Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {10[T], 12[T]}, {11[T]}, {12[T]}] Covered Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {10[T], 12[T]}, {11[T], 12[T]}] Step with 10 Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)], 10[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {10[T], 12[T]}, {11[T], 12[T]}, {}] Covered Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)], 11[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {10[T], 12[T]}, {10[T], 11[T], 12[T]}] Backtrack Trace 9[T], 11[(1-x^0 <= 0)], 12[(-1+n >= 0 /\ -n+x^0 >= 0)] Blocked [{}, {10[T], 12[T]}, {11[T]}, {10[T], 11[T], 12[T]}] Backtrack Trace 9[T], 11[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {11[T], 12[T]}] Step with 10 Trace 9[T], 11[(1-x^0 <= 0)], 10[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {11[T], 12[T]}, {}] Covered Trace 9[T], 11[(1-x^0 <= 0)] Blocked [{}, {10[T], 12[T]}, {10[T], 11[T], 12[T]}] Backtrack Trace 9[T] Blocked [{}, {10[T], 11[T], 12[T]}] Backtrack Trace Blocked [{9[T]}] Accept unknown Build SHA: a05f16bf13df659c382799650051f91bf6828c7b