YES(?, 11*b + 4*b^2 + 7) Initial complexity problem: 1: T: (1, 1) l0(a, b, c, d) -> l1(0, b, c, d) (?, 1) l1(a, b, c, d) -> l2(a, b, 0, 0) [ b >= 1 ] (?, 1) l2(a, b, c, d) -> l2(a, b, c + 1, d + c) [ b >= c + 1 ] (?, 1) l2(a, b, c, d) -> l1(a + d, b - 1, c, d) [ c >= b ] start location: l0 leaf cost: 0 Separating problem 1 produces the isolated subproblem 10001: T: (1, 0) inner_10000_start_sep(a, b, c, d) -> l2(a, b, 0, 0) (?, 1) l2(a, b, c, d) -> l2(a, b, c + 1, d + c) [ b >= c + 1 ] start location: inner_10000_start_sep leaf cost: 0 === begin of proof for isolated subproblem 10001 === Initial complexity problem: 10001: T: (1, 0) inner_10000_start_sep(a, b, c, d) -> l2(a, b, 0, 0) (?, 1) l2(a, b, c, d) -> l2(a, b, c + 1, d + c) [ b >= c + 1 ] start location: inner_10000_start_sep leaf cost: 0 A polynomial rank function with Pol(inner_10000_start_sep) = V_2 Pol(l2) = V_2 - V_3 orients all transitions weakly and the transition l2(a, b, c, d) -> l2(a, b, c + 1, d + c) [ b >= c + 1 ] strictly and produces the following problem: 10002: T: (1, 0) inner_10000_start_sep(a, b, c, d) -> l2(a, b, 0, 0) (b, 1) l2(a, b, c, d) -> l2(a, b, c + 1, d + c) [ b >= c + 1 ] start location: inner_10000_start_sep leaf cost: 0 === end of proof for isolated subproblem 10001 === Applying the information from the isolated subproblem 10001 to problem 1 produces the following problem: 2: T: (?, 0) inner_10000_in_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c, d) (?, b) inner_10000_in_sep(a, b, c, d) -> inner_10000_compl_sep(a, b, c, d) (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ d_sep >= 0 /\ b >= 0 /\ c_sep >= 0 /\ d_sep <= b + b^2 /\ c_sep <= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ d_sep >= 0 /\ b >= 0 /\ c_sep < 0 /\ d_sep <= b + b^2 /\ -c_sep <= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ d_sep >= 0 /\ b < 0 /\ c_sep >= 0 /\ d_sep <= -b + b^2 /\ c_sep <= -b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ d_sep >= 0 /\ b < 0 /\ c_sep < 0 /\ d_sep <= -b + b^2 /\ -c_sep <= -b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ d_sep < 0 /\ b >= 0 /\ c_sep >= 0 /\ -d_sep <= b + b^2 /\ c_sep <= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ d_sep < 0 /\ b >= 0 /\ c_sep < 0 /\ -d_sep <= b + b^2 /\ -c_sep <= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ d_sep < 0 /\ b < 0 /\ c_sep >= 0 /\ -d_sep <= -b + b^2 /\ c_sep <= -b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ d_sep < 0 /\ b < 0 /\ c_sep < 0 /\ -d_sep <= -b + b^2 /\ -c_sep <= -b ] (?, 1) inner_10000_out_sep(a, b, c, d) -> l1(a + d, b - 1, c, d) [ c >= b ] (?, 1) l1(a, b, c, d) -> inner_10000_in_sep(a, b, 0, 0) [ b >= 1 ] (1, 1) l0(a, b, c, d) -> l1(0, b, c, d) start location: l0 leaf cost: 0 Applied AI with 'oct' on problem 2 to obtain the following invariants: For symbol inner_10000_compl_sep: -X_4 >= 0 /\ X_3 - X_4 >= 0 /\ -X_3 - X_4 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ -X_3 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 For symbol inner_10000_in_sep: -X_4 >= 0 /\ X_3 - X_4 >= 0 /\ -X_3 - X_4 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ -X_3 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 For symbol inner_10000_out_sep: X_2 - X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_2 - 1 >= 0 This yielded the following problem: 3: T: (1, 1) l0(a, b, c, d) -> l1(0, b, c, d) (?, 1) l1(a, b, c, d) -> inner_10000_in_sep(a, b, 0, 0) [ b >= 1 ] (?, 1) inner_10000_out_sep(a, b, c, d) -> l1(a + d, b - 1, c, d) [ b - c >= 0 /\ b + c >= 0 /\ b - 1 >= 0 /\ c >= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b < 0 /\ c_sep < 0 /\ -d_sep <= -b + b^2 /\ -c_sep <= -b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b < 0 /\ c_sep >= 0 /\ -d_sep <= -b + b^2 /\ c_sep <= -b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b >= 0 /\ c_sep < 0 /\ -d_sep <= b + b^2 /\ -c_sep <= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b >= 0 /\ c_sep >= 0 /\ -d_sep <= b + b^2 /\ c_sep <= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b < 0 /\ c_sep < 0 /\ d_sep <= -b + b^2 /\ -c_sep <= -b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b < 0 /\ c_sep >= 0 /\ d_sep <= -b + b^2 /\ c_sep <= -b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b >= 0 /\ c_sep < 0 /\ d_sep <= b + b^2 /\ -c_sep <= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b >= 0 /\ c_sep >= 0 /\ d_sep <= b + b^2 /\ c_sep <= b ] (?, b) inner_10000_in_sep(a, b, c, d) -> inner_10000_compl_sep(a, b, c, d) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 ] (?, 0) inner_10000_in_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c, d) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 ] start location: l0 leaf cost: 0 Testing for unsatisfiable constraints removes the following transitions from problem 3: inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b < 0 /\ c_sep < 0 /\ -d_sep <= -b + b^2 /\ -c_sep <= -b ] inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b < 0 /\ c_sep >= 0 /\ -d_sep <= -b + b^2 /\ c_sep <= -b ] inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b < 0 /\ c_sep < 0 /\ d_sep <= -b + b^2 /\ -c_sep <= -b ] inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b < 0 /\ c_sep >= 0 /\ d_sep <= -b + b^2 /\ c_sep <= -b ] We thus obtain the following problem: 4: T: (1, 1) l0(a, b, c, d) -> l1(0, b, c, d) (?, 1) l1(a, b, c, d) -> inner_10000_in_sep(a, b, 0, 0) [ b >= 1 ] (?, 1) inner_10000_out_sep(a, b, c, d) -> l1(a + d, b - 1, c, d) [ b - c >= 0 /\ b + c >= 0 /\ b - 1 >= 0 /\ c >= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b >= 0 /\ c_sep < 0 /\ -d_sep <= b + b^2 /\ -c_sep <= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b >= 0 /\ c_sep >= 0 /\ -d_sep <= b + b^2 /\ c_sep <= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b >= 0 /\ c_sep < 0 /\ d_sep <= b + b^2 /\ -c_sep <= b ] (?, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b >= 0 /\ c_sep >= 0 /\ d_sep <= b + b^2 /\ c_sep <= b ] (?, b) inner_10000_in_sep(a, b, c, d) -> inner_10000_compl_sep(a, b, c, d) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 ] (?, 0) inner_10000_in_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c, d) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 ] start location: l0 leaf cost: 0 A polynomial rank function with Pol(l0) = 4*V_2 + 3 Pol(l1) = 4*V_2 + 3 Pol(inner_10000_in_sep) = 4*V_2 + 2 Pol(inner_10000_out_sep) = 4*V_2 Pol(inner_10000_compl_sep) = 4*V_2 + 1 orients all transitions weakly and the transitions l1(a, b, c, d) -> inner_10000_in_sep(a, b, 0, 0) [ b >= 1 ] inner_10000_out_sep(a, b, c, d) -> l1(a + d, b - 1, c, d) [ b - c >= 0 /\ b + c >= 0 /\ b - 1 >= 0 /\ c >= b ] inner_10000_in_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c, d) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 ] inner_10000_in_sep(a, b, c, d) -> inner_10000_compl_sep(a, b, c, d) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 ] inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b >= 0 /\ c_sep < 0 /\ -d_sep <= b + b^2 /\ -c_sep <= b ] inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b >= 0 /\ c_sep >= 0 /\ -d_sep <= b + b^2 /\ c_sep <= b ] inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b >= 0 /\ c_sep < 0 /\ d_sep <= b + b^2 /\ -c_sep <= b ] inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b >= 0 /\ c_sep >= 0 /\ d_sep <= b + b^2 /\ c_sep <= b ] strictly and produces the following problem: 5: T: (1, 1) l0(a, b, c, d) -> l1(0, b, c, d) (4*b + 3, 1) l1(a, b, c, d) -> inner_10000_in_sep(a, b, 0, 0) [ b >= 1 ] (4*b + 3, 1) inner_10000_out_sep(a, b, c, d) -> l1(a + d, b - 1, c, d) [ b - c >= 0 /\ b + c >= 0 /\ b - 1 >= 0 /\ c >= b ] (4*b + 3, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b >= 0 /\ c_sep < 0 /\ -d_sep <= b + b^2 /\ -c_sep <= b ] (4*b + 3, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep < 0 /\ b >= 0 /\ c_sep >= 0 /\ -d_sep <= b + b^2 /\ c_sep <= b ] (4*b + 3, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b >= 0 /\ c_sep < 0 /\ d_sep <= b + b^2 /\ -c_sep <= b ] (4*b + 3, 0) inner_10000_compl_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c_sep, d_sep) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 /\ d_sep >= 0 /\ b >= 0 /\ c_sep >= 0 /\ d_sep <= b + b^2 /\ c_sep <= b ] (4*b + 3, b) inner_10000_in_sep(a, b, c, d) -> inner_10000_compl_sep(a, b, c, d) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 ] (4*b + 3, 0) inner_10000_in_sep(a, b, c, d) -> inner_10000_out_sep(a, b, c, d) [ -d >= 0 /\ c - d >= 0 /\ -c - d >= 0 /\ b - d - 1 >= 0 /\ d >= 0 /\ c + d >= 0 /\ -c + d >= 0 /\ b + d - 1 >= 0 /\ -c >= 0 /\ b - c - 1 >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ b - 1 >= 0 ] start location: l0 leaf cost: 0 Complexity upper bound 11*b + 4*b^2 + 7 Time: 0.812 sec (SMT: 0.760 sec)