YES(?, 132*b + 72*b^2 + 64) Initial complexity problem: 1: T: (1, 1) evalrealselectstart(a, b, c) -> evalrealselectentryin(a, b, c) (?, 1) evalrealselectentryin(a, b, c) -> evalrealselectbb6in(0, b, c) (?, 1) evalrealselectbb6in(a, b, c) -> evalrealselectbbin(a, b, c) [ b >= a + 2 ] (?, 1) evalrealselectbb6in(a, b, c) -> evalrealselectreturnin(a, b, c) [ a + 1 >= b ] (?, 1) evalrealselectbbin(a, b, c) -> evalrealselectbb4in(a, b, a + 1) (?, 1) evalrealselectbb4in(a, b, c) -> evalrealselectbb1in(a, b, c) [ b >= c + 1 ] (?, 1) evalrealselectbb4in(a, b, c) -> evalrealselectbb5in(a, b, c) [ c >= b ] (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ d >= e + 1 ] (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ e >= d ] (?, 1) evalrealselectbb5in(a, b, c) -> evalrealselectbb6in(a + 1, b, c) (?, 1) evalrealselectreturnin(a, b, c) -> evalrealselectstop(a, b, c) start location: evalrealselectstart leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) evalrealselectstart(a, b, c) -> evalrealselectentryin(a, b, c) (?, 1) evalrealselectentryin(a, b, c) -> evalrealselectbb6in(0, b, c) (?, 1) evalrealselectbb6in(a, b, c) -> evalrealselectbbin(a, b, c) [ b >= a + 2 ] (?, 1) evalrealselectbbin(a, b, c) -> evalrealselectbb4in(a, b, a + 1) (?, 1) evalrealselectbb4in(a, b, c) -> evalrealselectbb1in(a, b, c) [ b >= c + 1 ] (?, 1) evalrealselectbb4in(a, b, c) -> evalrealselectbb5in(a, b, c) [ c >= b ] (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ d >= e + 1 ] (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ e >= d ] (?, 1) evalrealselectbb5in(a, b, c) -> evalrealselectbb6in(a + 1, b, c) start location: evalrealselectstart leaf cost: 2 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) evalrealselectstart(a, b, c) -> evalrealselectentryin(a, b, c) (1, 1) evalrealselectentryin(a, b, c) -> evalrealselectbb6in(0, b, c) (?, 1) evalrealselectbb6in(a, b, c) -> evalrealselectbbin(a, b, c) [ b >= a + 2 ] (?, 1) evalrealselectbbin(a, b, c) -> evalrealselectbb4in(a, b, a + 1) (?, 1) evalrealselectbb4in(a, b, c) -> evalrealselectbb1in(a, b, c) [ b >= c + 1 ] (?, 1) evalrealselectbb4in(a, b, c) -> evalrealselectbb5in(a, b, c) [ c >= b ] (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ d >= e + 1 ] (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ e >= d ] (?, 1) evalrealselectbb5in(a, b, c) -> evalrealselectbb6in(a + 1, b, c) start location: evalrealselectstart leaf cost: 2 Separating problem 3 produces the isolated subproblem 10001: T: (1, 0) inner_10000_start_sep(a, b, c) -> evalrealselectbb4in(a, b, a + 1) (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ e >= d ] (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ d >= e + 1 ] (?, 1) evalrealselectbb4in(a, b, c) -> evalrealselectbb1in(a, b, 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) -> evalrealselectbb4in(a, b, a + 1) (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ e >= d ] (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ d >= e + 1 ] (?, 1) evalrealselectbb4in(a, b, c) -> evalrealselectbb1in(a, b, c) [ b >= c + 1 ] start location: inner_10000_start_sep leaf cost: 0 A polynomial rank function with Pol(inner_10000_start_sep) = -2*V_1 + 2*V_2 - 2 Pol(evalrealselectbb4in) = 2*V_2 - 2*V_3 Pol(evalrealselectbb1in) = 2*V_2 - 2*V_3 - 1 orients all transitions weakly and the transition evalrealselectbb4in(a, b, c) -> evalrealselectbb1in(a, b, c) [ b >= c + 1 ] strictly and produces the following problem: 10002: T: (1, 0) inner_10000_start_sep(a, b, c) -> evalrealselectbb4in(a, b, a + 1) (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ e >= d ] (?, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ d >= e + 1 ] (2*a + 2*b + 2, 1) evalrealselectbb4in(a, b, c) -> evalrealselectbb1in(a, b, c) [ b >= c + 1 ] start location: inner_10000_start_sep leaf cost: 0 Repeatedly propagating knowledge in problem 10002 produces the following problem: 10003: T: (1, 0) inner_10000_start_sep(a, b, c) -> evalrealselectbb4in(a, b, a + 1) (2*a + 2*b + 2, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ e >= d ] (2*a + 2*b + 2, 1) evalrealselectbb1in(a, b, c) -> evalrealselectbb4in(a, b, c + 1) [ d >= e + 1 ] (2*a + 2*b + 2, 1) evalrealselectbb4in(a, b, c) -> evalrealselectbb1in(a, b, 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 3 produces the following problem: 4: T: (?, 0) inner_10000_in_sep(a, b, c) -> inner_10000_out_sep(a, b, c) (?, 6*a + 6*b + 6) inner_10000_in_sep(a, b, c) -> inner_10000_compl_sep(a, b, c) (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b >= 0 /\ a >= 0 /\ c_sep >= 0 /\ c_sep <= 5*a + 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b >= 0 /\ a >= 0 /\ c_sep < 0 /\ -c_sep <= 5*a + 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b >= 0 /\ a < 0 /\ c_sep >= 0 /\ c_sep <= -5*a + 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b >= 0 /\ a < 0 /\ c_sep < 0 /\ -c_sep <= -5*a + 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b < 0 /\ a >= 0 /\ c_sep >= 0 /\ c_sep <= 5*a - 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b < 0 /\ a >= 0 /\ c_sep < 0 /\ -c_sep <= 5*a - 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b < 0 /\ a < 0 /\ c_sep >= 0 /\ c_sep <= -5*a - 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b < 0 /\ a < 0 /\ c_sep < 0 /\ -c_sep <= -5*a - 5*b + 125 ] (?, 1) inner_10000_out_sep(a, b, c) -> evalrealselectbb5in(a, b, c) [ c >= b ] (?, 1) evalrealselectbbin(a, b, c) -> inner_10000_in_sep(a, b, a + 1) (?, 1) evalrealselectbb5in(a, b, c) -> evalrealselectbb6in(a + 1, b, c) (?, 1) evalrealselectbb6in(a, b, c) -> evalrealselectbbin(a, b, c) [ b >= a + 2 ] (1, 1) evalrealselectentryin(a, b, c) -> evalrealselectbb6in(0, b, c) (1, 1) evalrealselectstart(a, b, c) -> evalrealselectentryin(a, b, c) start location: evalrealselectstart leaf cost: 2 Applied AI with 'oct' on problem 4 to obtain the following invariants: For symbol evalrealselectbb5in: X_3 - 2 >= 0 /\ X_2 + X_3 - 4 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ -X_1 + X_3 - 2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalrealselectbb6in: X_1 >= 0 For symbol evalrealselectbbin: X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol inner_10000_compl_sep: X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 + 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol inner_10000_in_sep: X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 + 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol inner_10000_out_sep: X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 This yielded the following problem: 5: T: (1, 1) evalrealselectstart(a, b, c) -> evalrealselectentryin(a, b, c) (1, 1) evalrealselectentryin(a, b, c) -> evalrealselectbb6in(0, b, c) (?, 1) evalrealselectbb6in(a, b, c) -> evalrealselectbbin(a, b, c) [ a >= 0 /\ b >= a + 2 ] (?, 1) evalrealselectbb5in(a, b, c) -> evalrealselectbb6in(a + 1, b, c) [ c - 2 >= 0 /\ b + c - 4 >= 0 /\ -b + c >= 0 /\ a + c - 2 >= 0 /\ -a + c - 2 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] (?, 1) evalrealselectbbin(a, b, c) -> inner_10000_in_sep(a, b, a + 1) [ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] (?, 1) inner_10000_out_sep(a, b, c) -> evalrealselectbb5in(a, b, c) [ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ c >= b ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b < 0 /\ a < 0 /\ c_sep < 0 /\ -c_sep <= -5*a - 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b < 0 /\ a < 0 /\ c_sep >= 0 /\ c_sep <= -5*a - 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b < 0 /\ c_sep < 0 /\ -c_sep <= 5*a - 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b < 0 /\ c_sep >= 0 /\ c_sep <= 5*a - 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ a < 0 /\ c_sep < 0 /\ -c_sep <= -5*a + 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ a < 0 /\ c_sep >= 0 /\ c_sep <= -5*a + 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ c_sep < 0 /\ -c_sep <= 5*a + 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ c_sep >= 0 /\ c_sep <= 5*a + 5*b + 125 ] (?, 6*a + 6*b + 6) inner_10000_in_sep(a, b, c) -> inner_10000_compl_sep(a, b, c) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] (?, 0) inner_10000_in_sep(a, b, c) -> inner_10000_out_sep(a, b, c) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] start location: evalrealselectstart leaf cost: 2 Testing for unsatisfiable constraints removes the following transitions from problem 5: inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b < 0 /\ a < 0 /\ c_sep < 0 /\ -c_sep <= -5*a - 5*b + 125 ] inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b < 0 /\ a < 0 /\ c_sep >= 0 /\ c_sep <= -5*a - 5*b + 125 ] inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b < 0 /\ c_sep < 0 /\ -c_sep <= 5*a - 5*b + 125 ] inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b < 0 /\ c_sep >= 0 /\ c_sep <= 5*a - 5*b + 125 ] inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ a < 0 /\ c_sep < 0 /\ -c_sep <= -5*a + 5*b + 125 ] inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ a < 0 /\ c_sep >= 0 /\ c_sep <= -5*a + 5*b + 125 ] We thus obtain the following problem: 6: T: (1, 1) evalrealselectstart(a, b, c) -> evalrealselectentryin(a, b, c) (1, 1) evalrealselectentryin(a, b, c) -> evalrealselectbb6in(0, b, c) (?, 1) evalrealselectbb6in(a, b, c) -> evalrealselectbbin(a, b, c) [ a >= 0 /\ b >= a + 2 ] (?, 1) evalrealselectbb5in(a, b, c) -> evalrealselectbb6in(a + 1, b, c) [ c - 2 >= 0 /\ b + c - 4 >= 0 /\ -b + c >= 0 /\ a + c - 2 >= 0 /\ -a + c - 2 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] (?, 1) evalrealselectbbin(a, b, c) -> inner_10000_in_sep(a, b, a + 1) [ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] (?, 1) inner_10000_out_sep(a, b, c) -> evalrealselectbb5in(a, b, c) [ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ c >= b ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ c_sep < 0 /\ -c_sep <= 5*a + 5*b + 125 ] (?, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ c_sep >= 0 /\ c_sep <= 5*a + 5*b + 125 ] (?, 6*a + 6*b + 6) inner_10000_in_sep(a, b, c) -> inner_10000_compl_sep(a, b, c) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] (?, 0) inner_10000_in_sep(a, b, c) -> inner_10000_out_sep(a, b, c) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] start location: evalrealselectstart leaf cost: 2 A polynomial rank function with Pol(evalrealselectstart) = 6*V_2 - 6 Pol(evalrealselectentryin) = 6*V_2 - 6 Pol(evalrealselectbb6in) = -6*V_1 + 6*V_2 - 6 Pol(evalrealselectbbin) = -6*V_1 + 6*V_2 - 7 Pol(evalrealselectbb5in) = -6*V_1 + 6*V_2 - 11 Pol(inner_10000_in_sep) = -6*V_1 + 6*V_2 - 8 Pol(inner_10000_out_sep) = -6*V_1 + 6*V_2 - 10 Pol(inner_10000_compl_sep) = -6*V_1 + 6*V_2 - 9 orients all transitions weakly and the transitions inner_10000_out_sep(a, b, c) -> evalrealselectbb5in(a, b, c) [ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ c >= b ] inner_10000_in_sep(a, b, c) -> inner_10000_out_sep(a, b, c) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] inner_10000_in_sep(a, b, c) -> inner_10000_compl_sep(a, b, c) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ c_sep < 0 /\ -c_sep <= 5*a + 5*b + 125 ] inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ c_sep >= 0 /\ c_sep <= 5*a + 5*b + 125 ] evalrealselectbbin(a, b, c) -> inner_10000_in_sep(a, b, a + 1) [ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] evalrealselectbb6in(a, b, c) -> evalrealselectbbin(a, b, c) [ a >= 0 /\ b >= a + 2 ] evalrealselectbb5in(a, b, c) -> evalrealselectbb6in(a + 1, b, c) [ c - 2 >= 0 /\ b + c - 4 >= 0 /\ -b + c >= 0 /\ a + c - 2 >= 0 /\ -a + c - 2 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] strictly and produces the following problem: 7: T: (1, 1) evalrealselectstart(a, b, c) -> evalrealselectentryin(a, b, c) (1, 1) evalrealselectentryin(a, b, c) -> evalrealselectbb6in(0, b, c) (6*b + 6, 1) evalrealselectbb6in(a, b, c) -> evalrealselectbbin(a, b, c) [ a >= 0 /\ b >= a + 2 ] (6*b + 6, 1) evalrealselectbb5in(a, b, c) -> evalrealselectbb6in(a + 1, b, c) [ c - 2 >= 0 /\ b + c - 4 >= 0 /\ -b + c >= 0 /\ a + c - 2 >= 0 /\ -a + c - 2 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] (6*b + 6, 1) evalrealselectbbin(a, b, c) -> inner_10000_in_sep(a, b, a + 1) [ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] (6*b + 6, 1) inner_10000_out_sep(a, b, c) -> evalrealselectbb5in(a, b, c) [ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ c >= b ] (6*b + 6, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ c_sep < 0 /\ -c_sep <= 5*a + 5*b + 125 ] (6*b + 6, 0) inner_10000_compl_sep(a, b, c) -> inner_10000_out_sep(a, b, c_sep) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 /\ b >= 0 /\ c_sep >= 0 /\ c_sep <= 5*a + 5*b + 125 ] (6*b + 6, 6*a + 6*b + 6) inner_10000_in_sep(a, b, c) -> inner_10000_compl_sep(a, b, c) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] (6*b + 6, 0) inner_10000_in_sep(a, b, c) -> inner_10000_out_sep(a, b, c) [ b - c - 1 >= 0 /\ a - c + 1 >= 0 /\ c - 1 >= 0 /\ b + c - 3 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 2 >= 0 /\ a + b - 2 >= 0 /\ -a + b - 2 >= 0 /\ a >= 0 ] start location: evalrealselectstart leaf cost: 2 Complexity upper bound 132*b + 72*b^2 + 64 Time: 0.630 sec (SMT: 0.588 sec)