YES(?, 28*d + 7*g + 27) Initial complexity problem: 1: T: (1, 1) evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g) (?, 1) evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g) (?, 1) evalfbb5in(a, b, c, d, e, f, g) -> evalfreturnin(a, b, c, d, e, f, g) [ c >= d ] (?, 1) evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g) (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ] (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ] (?, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] (?, 1) evalfreturnin(a, b, c, d, e, f, g) -> evalfstop(a, b, c, d, e, f, g) 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, g) -> evalfentryin(a, b, c, d, e, f, g) (?, 1) evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g) (?, 1) evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g) (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ] (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ] (?, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] 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, g) -> evalfentryin(a, b, c, d, e, f, g) (1, 1) evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g) (?, 1) evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g) (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ] (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ] (?, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] start location: evalfstart leaf cost: 2 A polynomial rank function with Pol(evalfstart) = 3*V_7 - 1 Pol(evalfentryin) = 3*V_7 - 1 Pol(evalfbb5in) = -3*V_1 + 3*V_7 - 1 Pol(evalfbbin) = -3*V_1 + 3*V_7 - 1 Pol(evalfbb1in) = -3*V_1 + 3*V_7 - 1 Pol(evalfbb3in) = -3*V_6 + 3*V_7 - 2 orients all transitions weakly and the transition evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] strictly and produces the following problem: 4: T: (1, 1) evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g) (1, 1) evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g) (?, 1) evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g) (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ] (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ] (3*g + 1, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] start location: evalfstart leaf cost: 2 A polynomial rank function with Pol(evalfstart) = 4*V_4 - 3 Pol(evalfentryin) = 4*V_4 - 3 Pol(evalfbb5in) = -4*V_3 + 4*V_4 - 3 Pol(evalfbbin) = 4*V_4 - 4*V_5 - 1 Pol(evalfbb1in) = 4*V_4 - 4*V_5 - 2 Pol(evalfbb3in) = 4*V_4 - 4*V_5 - 2 orients all transitions weakly and the transition evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ] strictly and produces the following problem: 5: T: (1, 1) evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g) (1, 1) evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g) (4*d + 3, 1) evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ] (?, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g) (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ] (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] (?, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ] (3*g + 1, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] start location: evalfstart leaf cost: 2 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (1, 1) evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g) (1, 1) evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g) (4*d + 3, 1) evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ] (4*d + 3, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ] (4*d + 3, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ] (4*d + 3, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g) (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ] (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] (3*g + 4*d + 4, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ] (3*g + 1, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] start location: evalfstart leaf cost: 2 A polynomial rank function with Pol(evalfbb1in) = 1 Pol(evalfbb5in) = 0 and size complexities S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-0) = 6*d + 6*g + 6480 S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-1) = ? S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-2) = 4*d + 3072 S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-3) = d S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-4) = 4*d + 48 S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-5) = 6*d + 6*g + 180 S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-6) = g S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ]", 0-0) = 6*d + 6*g + 180 S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ]", 0-1) = ? S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ]", 0-2) = 4*d + 48 S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ]", 0-3) = d S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ]", 0-4) = 4*d + 192 S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ]", 0-5) = 6*d + 6*g + 1080 S("evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ]", 0-6) = g S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-0) = 6*d + 6*g + 180 S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-1) = ? S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-2) = 4*d + 3072 S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-3) = d S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-4) = 4*d + 48 S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-5) = ? S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ]", 0-6) = g S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ]", 0-0) = 6*d + 6*g + 180 S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ]", 0-1) = ? S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ]", 0-2) = 4*d + 48 S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ]", 0-3) = d S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ]", 0-4) = 4*d + 192 S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ]", 0-5) = ? S("evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ]", 0-6) = g S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g)", 0-0) = 6*d + 6*g + 1080 S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g)", 0-1) = ? S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g)", 0-2) = 4*d + 768 S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g)", 0-3) = d S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g)", 0-4) = 4*d + 48 S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g)", 0-5) = 6*d + 6*g + 180 S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g)", 0-6) = g S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ]", 0-0) = 6*d + 6*g + 180 S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ]", 0-1) = ? S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ]", 0-2) = 4*d + 768 S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ]", 0-3) = d S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ]", 0-4) = 4*d + 48 S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ]", 0-5) = ? S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ]", 0-6) = g S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ]", 0-0) = 6*d + 6*g + 180 S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ]", 0-1) = ? S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ]", 0-2) = 4*d + 768 S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ]", 0-3) = d S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ]", 0-4) = 4*d + 48 S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ]", 0-5) = ? S("evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ]", 0-6) = g S("evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ]", 0-0) = 6*d + 6*g + 180 S("evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ]", 0-1) = ? S("evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ]", 0-2) = 4*d + 192 S("evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ]", 0-3) = d S("evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ]", 0-4) = 4*d + 48 S("evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ]", 0-5) = ? S("evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ]", 0-6) = g S("evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g)", 0-0) = 0 S("evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g)", 0-1) = 0 S("evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g)", 0-2) = 0 S("evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g)", 0-3) = d S("evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g)", 0-4) = e S("evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g)", 0-5) = f S("evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g)", 0-6) = g S("evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g)", 0-0) = a S("evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g)", 0-1) = b S("evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g)", 0-2) = c S("evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g)", 0-3) = d S("evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g)", 0-4) = e S("evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g)", 0-5) = f S("evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g)", 0-6) = g orients the transitions evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ] evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] weakly and the transition evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ] strictly and produces the following problem: 7: T: (1, 1) evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g) (1, 1) evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g) (4*d + 3, 1) evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ] (4*d + 3, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ] (4*d + 3, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ] (4*d + 3, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g) (8*d + 6, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ] (?, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] (3*g + 4*d + 4, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ] (3*g + 1, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] start location: evalfstart leaf cost: 2 A polynomial rank function with Pol(evalfstart) = V_7 Pol(evalfentryin) = V_7 Pol(evalfbb5in) = -V_2 + V_7 Pol(evalfbbin) = -V_2 + V_7 Pol(evalfbb1in) = -V_6 + V_7 Pol(evalfbb3in) = -V_2 + V_7 orients all transitions weakly and the transition evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] strictly and produces the following problem: 8: T: (1, 1) evalfstart(a, b, c, d, e, f, g) -> evalfentryin(a, b, c, d, e, f, g) (1, 1) evalfentryin(a, b, c, d, e, f, g) -> evalfbb5in(0, 0, 0, d, e, f, g) (4*d + 3, 1) evalfbb5in(a, b, c, d, e, f, g) -> evalfbbin(a, b, c, d, c + 1, f, g) [ d >= c + 1 ] (4*d + 3, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ 0 >= h + 1 ] (4*d + 3, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, b, g) [ h >= 1 ] (4*d + 3, 1) evalfbbin(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, a, g) (8*d + 6, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb5in(a, f + 1, e, d, e, f, g) [ f >= g ] (g, 1) evalfbb1in(a, b, c, d, e, f, g) -> evalfbb1in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] (3*g + 4*d + 4, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb5in(f + 1, b, e, d, e, f, g) [ f >= g ] (3*g + 1, 1) evalfbb3in(a, b, c, d, e, f, g) -> evalfbb3in(a, b, c, d, e, f + 1, g) [ g >= f + 1 ] start location: evalfstart leaf cost: 2 Complexity upper bound 28*d + 7*g + 27 Time: 2.421 sec (SMT: 1.869 sec)