MAYBE Initial complexity problem: 1: T: (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) (?, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (?, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (?, 1) evalfbb8in(a, b, c, d, e, f) -> evalfreturnin(a, b, c, d, e, f) [ 0 >= b + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) (?, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) (?, 1) evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) (?, 1) evalfreturnin(a, b, c, d, e, f) -> evalfstop(a, b, c, d, e, f) start location: evalfstart leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) (?, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (?, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) (?, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) (?, 1) evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) start location: evalfstart leaf cost: 2 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (?, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) (?, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) (?, 1) evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) start location: evalfstart leaf cost: 2 A polynomial rank function with Pol(evalfstart) = 5*V_1 + 1 Pol(evalfentryin) = 5*V_1 + 1 Pol(evalfbb8in) = 5*V_2 + 1 Pol(evalfbb2in) = 5*V_2 - 1 Pol(evalfbb4in) = 5*V_2 - 2 Pol(evalfbb3in) = 5*V_2 - 1 Pol(evalfbb1in) = 5*V_2 - 1 Pol(evalfbb6in) = 5*V_4 + 2 Pol(evalfbb7in) = 5*V_4 + 2 Pol(evalfbb5in) = 5*V_4 + 2 orients all transitions weakly and the transition evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] strictly and produces the following problem: 4: T: (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) (?, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) (?, 1) evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) start location: evalfstart leaf cost: 2 A polynomial rank function with Pol(evalfbb7in) = 1 Pol(evalfbb8in) = 0 Pol(evalfbb5in) = 1 Pol(evalfbb6in) = 1 Pol(evalfbb4in) = 2 Pol(evalfbb3in) = 3 Pol(evalfbb1in) = 3 Pol(evalfbb2in) = 3 and size complexities S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-0) = ? S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-1) = ? S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-2) = ? S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-3) = ? S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-4) = ? S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-5) = f S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-0) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-1) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-2) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-3) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-4) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-5) = f S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-0) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-1) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-2) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-3) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-4) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-5) = f S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-0) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-1) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-2) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-3) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-4) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-5) = f S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-0) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-1) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-2) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-3) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-4) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-5) = f S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-0) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-1) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-2) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-3) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-4) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-5) = f S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-0) = ? S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-1) = ? S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-2) = ? S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-3) = ? S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-4) = ? S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-5) = f S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-0) = ? S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-1) = ? S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-2) = ? S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-3) = ? S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-4) = ? S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-5) = f S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-0) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-1) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-2) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-3) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-4) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-5) = f S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-0) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-1) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-2) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-3) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-4) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-5) = f S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-0) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-1) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-2) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-3) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-4) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-5) = f S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-0) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-1) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-2) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-3) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-4) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-5) = f S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-0) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-1) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-2) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-3) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-4) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-5) = f S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-0) = ? S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-1) = ? S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-2) = ? S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-3) = ? S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-4) = ? S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-5) = f S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-0) = b S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-1) = a S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-2) = c S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-3) = d S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-4) = e S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-5) = f S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-0) = a S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-1) = b S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-2) = c S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-3) = d S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-4) = e S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-5) = f orients the transitions evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ] evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ] evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ] evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ] evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ] evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ] evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ] evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ] evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) weakly and the transitions evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ] strictly and produces the following problem: 5: T: (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ] (15*a + 3, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) (?, 1) evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) start location: evalfstart leaf cost: 2 A polynomial rank function with Pol(evalfbb7in) = 1 Pol(evalfbb5in) = 1 Pol(evalfbb6in) = 1 Pol(evalfbb8in) = 0 Pol(evalfbb3in) = -1 Pol(evalfbb1in) = -1 Pol(evalfbb2in) = -1 and size complexities S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-0) = ? S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-1) = 16*a + 196608 S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-2) = ? S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-3) = 16*a + 768 S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-4) = ? S("evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f)", 0-5) = f S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-0) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-1) = 16*a + 768 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-2) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-3) = 16*a + 12288 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-4) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f)", 0-5) = f S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-0) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-1) = 16*a + 196608 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-2) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-3) = 16*a + 768 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-4) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ]", 0-5) = f S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-0) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-1) = 16*a + 196608 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-2) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-3) = 16*a + 768 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-4) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-5) = f S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-0) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-1) = 16*a + 196608 S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-2) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-3) = 16*a + 768 S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-4) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ]", 0-5) = f S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-0) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-1) = 16*a + 768 S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-2) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-3) = 16*a + 12288 S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-4) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ]", 0-5) = f S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-0) = ? S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-1) = 16*a + 12288 S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-2) = ? S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-3) = 16*a + 768 S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-4) = ? S("evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f)", 0-5) = f S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-0) = ? S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-1) = 16*a + 768 S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-2) = ? S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-3) = 16*a + 16*d + 3145728 S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-4) = ? S("evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f)", 0-5) = f S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-0) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-1) = 16*a + 768 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-2) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-3) = 16*a + 16*d + 50331648 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-4) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f)", 0-5) = f S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-0) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-1) = 16*a + 768 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-2) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-3) = 16*a + 16*d + 3145728 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-4) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ]", 0-5) = f S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-0) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-1) = 16*a + 768 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-2) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-3) = 16*a + 16*d + 3145728 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-4) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ]", 0-5) = f S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-0) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-1) = 16*a + 768 S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-2) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-3) = 16*a + 16*d + 3145728 S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-4) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ]", 0-5) = f S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-0) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-1) = 16*a + 768 S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-2) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-3) = 16*a + 16*d + 50331648 S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-4) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ]", 0-5) = f S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-0) = ? S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-1) = 16*a + 768 S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-2) = ? S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-3) = 16*a + 16*d + 196608 S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-4) = ? S("evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ]", 0-5) = f S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-0) = b S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-1) = a S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-2) = c S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-3) = d S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-4) = e S("evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f)", 0-5) = f S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-0) = a S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-1) = b S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-2) = c S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-3) = d S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-4) = e S("evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f)", 0-5) = f orients the transitions evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ] evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ] evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ] evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ] evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ] evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ] evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ] evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) weakly and the transition evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ] strictly and produces the following problem: 6: T: (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ c >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ g >= 1 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) (20*a + 4, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ e >= f + 1 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ f >= e ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ 0 >= g + 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ g >= 1 ] (15*a + 3, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) (?, 1) evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) start location: evalfstart leaf cost: 2 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol evalfbb1in: X_1 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfbb2in: X_1 - X_3 >= 0 /\ X_2 >= 0 For symbol evalfbb3in: X_1 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfbb4in: X_1 - X_3 >= 0 /\ X_2 >= 0 For symbol evalfbb5in: -X_5 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_3 + X_5 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_4 + 1 >= 0 /\ X_2 + X_4 + 1 >= 0 /\ -X_2 + X_4 + 1 >= 0 /\ X_1 - X_3 >= 0 /\ X_2 >= 0 For symbol evalfbb6in: -X_3 + X_5 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_4 + 1 >= 0 /\ X_2 + X_4 + 1 >= 0 /\ -X_2 + X_4 + 1 >= 0 /\ X_1 - X_3 >= 0 /\ X_2 >= 0 For symbol evalfbb7in: -X_5 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_3 + X_5 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_4 + 1 >= 0 /\ X_2 + X_4 + 1 >= 0 /\ -X_2 + X_4 + 1 >= 0 /\ X_1 - X_3 >= 0 /\ X_2 >= 0 This yielded the following problem: 7: T: (?, 1) evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 ] (15*a + 3, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (20*a + 4, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 By chaining the transition evalfbb7in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 ] with all transitions in problem 7, the following new transition is obtained: evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] We thus obtain the following problem: 8: T: (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (?, 1) evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (20*a + 4, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 By chaining the transition evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] with all transitions in problem 8, the following new transition is obtained: evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] We thus obtain the following problem: 9: T: (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (?, 1) evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (20*a + 4, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 By chaining the transition evalfbb7in(a, b, c, d, e, f) -> evalfbb5in(a, b, c, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] with all transitions in problem 9, the following new transition is obtained: evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] We thus obtain the following problem: 10: T: (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (?, 1) evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (20*a + 4, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 Testing for reachability in the complexity graph removes the following transition from problem 10: evalfbb5in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 ] We thus obtain the following problem: 11: T: (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (20*a + 4, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 By chaining the transition evalfbb6in(a, b, c, d, e, f) -> evalfbb8in(e, d, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 ] with all transitions in problem 11, the following new transition is obtained: evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] We thus obtain the following problem: 12: T: (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 By chaining the transition evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] with all transitions in problem 12, the following new transition is obtained: evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] We thus obtain the following problem: 13: T: (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (?, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 By chaining the transition evalfbb3in(a, b, c, d, e, f) -> evalfbb1in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] with all transitions in problem 13, the following new transition is obtained: evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] We thus obtain the following problem: 14: T: (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (?, 1) evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 Testing for reachability in the complexity graph removes the following transition from problem 14: evalfbb1in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] We thus obtain the following problem: 15: T: (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 1) evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 By chaining the transition evalfbb3in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] with all transitions in problem 15, the following new transition is obtained: evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] We thus obtain the following problem: 16: T: (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 By chaining the transition evalfbb2in(a, b, c, d, e, f) -> evalfbb4in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] with all transitions in problem 16, the following new transition is obtained: evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] We thus obtain the following problem: 17: T: (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 1) evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 Testing for reachability in the complexity graph removes the following transition from problem 17: evalfbb4in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 ] We thus obtain the following problem: 18: T: (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 By chaining the transition evalfentryin(a, b, c, d, e, f) -> evalfbb8in(b, a, c, d, e, f) with all transitions in problem 18, the following new transition is obtained: evalfentryin(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] We thus obtain the following problem: 19: T: (1, 2) evalfentryin(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (5*a + 1, 1) evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 Testing for reachability in the complexity graph removes the following transition from problem 19: evalfbb8in(a, b, c, d, e, f) -> evalfbb2in(a, b, a, d, e, f) [ b >= 0 ] We thus obtain the following problem: 20: T: (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (1, 2) evalfentryin(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] (1, 1) evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) start location: evalfstart leaf cost: 2 By chaining the transition evalfstart(a, b, c, d, e, f) -> evalfentryin(a, b, c, d, e, f) with all transitions in problem 20, the following new transition is obtained: evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] We thus obtain the following problem: 21: T: (1, 3) evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (1, 2) evalfentryin(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] start location: evalfstart leaf cost: 2 Testing for reachability in the complexity graph removes the following transition from problem 21: evalfentryin(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] We thus obtain the following problem: 22: T: (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (1, 3) evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] start location: evalfstart leaf cost: 2 By chaining the transition evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 ] with all transitions in problem 22, the following new transitions are obtained: evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 ] evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ f >= e + 1 ] We thus obtain the following problem: 23: T: (?, 4) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 ] (?, 3) evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ f >= e + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (1, 3) evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] start location: evalfstart leaf cost: 2 A polynomial rank function with Pol(evalfbb7in) = 1 Pol(evalfbb6in) = 1 Pol(evalfbb2in) = -1 Pol(evalfbb3in) = -1 and size complexities S("evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ]", 0-0) = b S("evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ]", 0-1) = a S("evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ]", 0-2) = b S("evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ]", 0-3) = d S("evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ]", 0-4) = e S("evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ]", 0-5) = f S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\\ b >= 0 /\\ c >= 0 ]", 0-0) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\\ b >= 0 /\\ c >= 0 ]", 0-1) = a + 2 S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\\ b >= 0 /\\ c >= 0 ]", 0-2) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\\ b >= 0 /\\ c >= 0 ]", 0-3) = a + d + 2 S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\\ b >= 0 /\\ c >= 0 ]", 0-4) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\\ b >= 0 /\\ c >= 0 ]", 0-5) = f S("evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ b >= 0 /\\ 0 >= c + 1 ]", 0-0) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ b >= 0 /\\ 0 >= c + 1 ]", 0-1) = a + 2 S("evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ b >= 0 /\\ 0 >= c + 1 ]", 0-2) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ b >= 0 /\\ 0 >= c + 1 ]", 0-3) = a + 2 S("evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ b >= 0 /\\ 0 >= c + 1 ]", 0-4) = ? S("evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ b >= 0 /\\ 0 >= c + 1 ]", 0-5) = f S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ 0 >= g + 1 ]", 0-0) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ 0 >= g + 1 ]", 0-1) = a + 2 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ 0 >= g + 1 ]", 0-2) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ 0 >= g + 1 ]", 0-3) = a + d + 2 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ 0 >= g + 1 ]", 0-4) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ 0 >= g + 1 ]", 0-5) = f S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ g >= 1 ]", 0-0) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ g >= 1 ]", 0-1) = a + 2 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ g >= 1 ]", 0-2) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ g >= 1 ]", 0-3) = a + d + 2 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ g >= 1 ]", 0-4) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 /\\ g >= 1 ]", 0-5) = f S("evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 ]", 0-0) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 ]", 0-1) = a + 2 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 ]", 0-2) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 ]", 0-3) = a + 2 S("evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 ]", 0-4) = ? S("evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\\ c >= 0 /\\ b + c >= 0 /\\ a + c >= 0 /\\ b >= 0 /\\ a + b >= 0 /\\ a >= 0 ]", 0-5) = f S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ f >= e ]", 0-0) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ f >= e ]", 0-1) = a + 2 S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ f >= e ]", 0-2) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ f >= e ]", 0-3) = a + 2 S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ f >= e ]", 0-4) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ f >= e ]", 0-5) = f S("evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ e >= f + 1 /\\ d >= 0 ]", 0-0) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ e >= f + 1 /\\ d >= 0 ]", 0-1) = a + 2 S("evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ e >= f + 1 /\\ d >= 0 ]", 0-2) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ e >= f + 1 /\\ d >= 0 ]", 0-3) = a + 2 S("evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ e >= f + 1 /\\ d >= 0 ]", 0-4) = ? S("evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ e >= f + 1 /\\ d >= 0 ]", 0-5) = f S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ d >= 0 ]", 0-0) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ d >= 0 ]", 0-1) = a + 2 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ d >= 0 ]", 0-2) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ d >= 0 ]", 0-3) = a + 2 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ d >= 0 ]", 0-4) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ d >= 0 ]", 0-5) = f S("evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ g >= 1 ]", 0-0) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ g >= 1 ]", 0-1) = a + 2 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ g >= 1 ]", 0-2) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ g >= 1 ]", 0-3) = a + 2 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ g >= 1 ]", 0-4) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ g >= 1 ]", 0-5) = f S("evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ f >= e + 1 ]", 0-0) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ f >= e + 1 ]", 0-1) = a + 2 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ f >= e + 1 ]", 0-2) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ f >= e + 1 ]", 0-3) = a + 2 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ f >= e + 1 ]", 0-4) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ f >= e + 1 ]", 0-5) = f S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ e + 1 >= f + 1 /\\ d >= 0 ]", 0-0) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ e + 1 >= f + 1 /\\ d >= 0 ]", 0-1) = a + 2 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ e + 1 >= f + 1 /\\ d >= 0 ]", 0-2) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ e + 1 >= f + 1 /\\ d >= 0 ]", 0-3) = a + 2 S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ e + 1 >= f + 1 /\\ d >= 0 ]", 0-4) = ? S("evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\\ -c + f >= 0 /\\ -c + e >= 0 /\\ b - d - 1 >= 0 /\\ d + 1 >= 0 /\\ b + d + 1 >= 0 /\\ -b + d + 1 >= 0 /\\ a - c >= 0 /\\ b >= 0 /\\ 0 >= g + 1 /\\ -c + e + 1 >= 0 /\\ e + 1 >= f + 1 /\\ d >= 0 ]", 0-5) = f orients the transitions evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ f >= e + 1 ] evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 ] evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] weakly and the transition evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 ] strictly and produces the following problem: 24: T: (65*a + 14, 4) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 ] (?, 3) evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ f >= e + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (1, 3) evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] start location: evalfstart leaf cost: 2 By chaining the transition evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 ] with all transitions in problem 24, the following new transitions are obtained: evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(e + 1, d, e + 1, d - 1, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 ] evalfbb7in(a, b, c, d, e, f) -> evalfbb3in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ e + 1 >= 0 ] We thus obtain the following problem: 25: T: (65*a + 14, 6) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(e + 1, d, e + 1, d - 1, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 ] (65*a + 14, 5) evalfbb7in(a, b, c, d, e, f) -> evalfbb3in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ e + 1 >= 0 ] (?, 3) evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ f >= e + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (1, 3) evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] start location: evalfstart leaf cost: 2 By chaining the transition evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(e + 1, d, e + 1, d - 1, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 ] with all transitions in problem 25, the following new transition is obtained: evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d - 1, e + 1, d - 1, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 /\ 2*d >= 0 /\ d - 1 >= 0 ] We thus obtain the following problem: 26: T: (65*a + 14, 8) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d - 1, e + 1, d - 1, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 /\ 2*d >= 0 /\ d - 1 >= 0 ] (65*a + 14, 5) evalfbb7in(a, b, c, d, e, f) -> evalfbb3in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ e + 1 >= 0 ] (?, 3) evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ f >= e + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (1, 3) evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] start location: evalfstart leaf cost: 2 By chaining the transition evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d - 1, e + 1, d - 1, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 /\ 2*d >= 0 /\ d - 1 >= 0 ] with all transitions in problem 26, the following new transition is obtained: evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(e + 1, d - 1, e + 1, d - 2, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 /\ 2*d >= 0 /\ d - 1 >= 0 ] We thus obtain the following problem: 27: T: (65*a + 14, 10) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(e + 1, d - 1, e + 1, d - 2, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 /\ 2*d >= 0 /\ d - 1 >= 0 ] (65*a + 14, 5) evalfbb7in(a, b, c, d, e, f) -> evalfbb3in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ e + 1 >= 0 ] (?, 3) evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ f >= e + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (1, 3) evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] start location: evalfstart leaf cost: 2 By chaining the transition evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(e + 1, d - 1, e + 1, d - 2, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 /\ 2*d >= 0 /\ d - 1 >= 0 ] with all transitions in problem 27, the following new transition is obtained: evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d - 2, e + 1, d - 2, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 /\ 2*d >= 0 /\ d - 1 >= 0 /\ 2*d - 2 >= 0 /\ d - 2 >= 0 ] We thus obtain the following problem: 28: T: (65*a + 14, 12) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e + 1, d - 2, e + 1, d - 2, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ 0 >= e + 2 /\ 2*d >= 0 /\ d - 1 >= 0 /\ 2*d - 2 >= 0 /\ d - 2 >= 0 ] (65*a + 14, 5) evalfbb7in(a, b, c, d, e, f) -> evalfbb3in(e + 1, d, e + 1, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ e + 1 >= f + 1 /\ d >= 0 /\ 0 >= 0 /\ e + 1 >= 0 ] (?, 3) evalfbb7in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ 0 >= g + 1 /\ -c + e + 1 >= 0 /\ f >= e + 1 ] (?, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, d, e + 1, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ g >= 1 ] (15*a + 3, 2) evalfbb7in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -e + f >= 0 /\ -c + f >= 0 /\ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ d >= 0 ] (20*a + 4, 2) evalfbb6in(a, b, c, d, e, f) -> evalfbb2in(e, d, e, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ e >= f + 1 /\ d >= 0 ] (?, 1) evalfbb6in(a, b, c, d, e, f) -> evalfbb7in(a, b, c, d, e, f) [ -c + e >= 0 /\ b - d - 1 >= 0 /\ d + 1 >= 0 /\ b + d + 1 >= 0 /\ -b + d + 1 >= 0 /\ a - c >= 0 /\ b >= 0 /\ f >= e ] (15*a + 3, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ g >= 1 ] (?, 2) evalfbb3in(a, b, c, d, e, f) -> evalfbb2in(a, b, c - 1, d, e, f) [ a - c >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ 0 >= g + 1 ] (15*a + 3, 2) evalfbb2in(a, b, c, d, e, f) -> evalfbb6in(a, b, c, b - 1, c, f) [ a - c >= 0 /\ b >= 0 /\ 0 >= c + 1 ] (?, 1) evalfbb2in(a, b, c, d, e, f) -> evalfbb3in(a, b, c, d, e, f) [ a - c >= 0 /\ b >= 0 /\ c >= 0 ] (1, 3) evalfstart(a, b, c, d, e, f) -> evalfbb2in(b, a, b, d, e, f) [ a >= 0 ] start location: evalfstart leaf cost: 2 Complexity upper bound ? Time: 5.157 sec (SMT: 4.607 sec)