YES(?, 2318416846246180*a + 2318416846246176*b + 4*e + 55800*a^2 + 110700*a*b + 54900*b^2 + 54900*a*e + 54900*b*e + 4) Initial complexity problem: 1: T: (?, 1) f2(a, b, c, d, e, f, g, h) -> f8(a, b, 0, b, e, f, g, h) [ a >= b + 1 ] (?, 1) f8(a, b, c, d, e, f, g, h) -> f8(a, b, c, d, e + 1, j, i, h) [ a >= e /\ i >= j ] (?, 1) f8(a, b, c, d, e, f, g, h) -> f8(a, b, j, e, e + 1, i, k, h) [ a >= e /\ i >= k + 1 ] (?, 1) f19(a, b, c, d, e, f, g, h) -> f19(a, b, c, d, e + 1, f, g, j) [ a >= e ] (?, 1) f27(a, b, c, d, e, f, g, h) -> f27(a, b, c, d, e + 1, f, g, j) [ a >= e ] (?, 1) f34(a, b, c, d, e, f, g, h) -> f36(a, b, c, d, e, f, g, h) [ 0 >= c + 1 ] (?, 1) f34(a, b, c, d, e, f, g, h) -> f36(a, b, c, d, e, f, g, h) [ c >= 1 ] (?, 1) f36(a, b, c, d, e, f, g, h) -> f43(a, b, c, d, e, f, g, j) [ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e, f, g, h) -> f43(a, b, c, d, e, f, g, j) [ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f43(a, b, c, d, e, f, g, h) -> f43(a, b, c, d, e + 1, f, g, h) [ a >= e ] (?, 1) f49(a, b, c, d, e, f, g, h) -> f49(a, b, c, d, e + 1, f, g, h) [ a >= e ] (?, 1) f36(a, b, c, d, e, f, g, h) -> f36(a, b, c, d + 1, e, f, g, 0) [ a >= d ] (?, 1) f34(a, b, c, d, e, f, g, h) -> f2(a, b + 1, 0, d, e, f, g, h) [ c = 0 ] (?, 1) f49(a, b, c, d, e, f, g, h) -> f36(a, b, c, d + 1, e, f, g, h) [ e >= a + 1 ] (?, 1) f43(a, b, c, d, e, f, g, h) -> f49(a, b, c, d, e, f, g, h) [ e >= a + 1 ] (?, 1) f36(a, b, c, d, e, f, g, h) -> f2(a, b + 1, c, d, e, f, g, h) [ d >= a + 1 ] (?, 1) f27(a, b, c, d, e, f, g, h) -> f34(a, b, c, d, e, f, g, h) [ e >= a + 1 ] (?, 1) f19(a, b, c, d, e, f, g, h) -> f27(a, b, c, d, e, f, g, h) [ e >= a + 1 ] (?, 1) f8(a, b, c, d, e, f, g, h) -> f34(a, b, c, b, e, f, g, h) [ e >= a + 1 /\ b = d ] (?, 1) f8(a, b, c, d, e, f, g, h) -> f19(a, b, c, d, e, f, g, h) [ b >= d + 1 /\ e >= a + 1 ] (?, 1) f8(a, b, c, d, e, f, g, h) -> f19(a, b, c, d, e, f, g, h) [ d >= b + 1 /\ e >= a + 1 ] (?, 1) f2(a, b, c, d, e, f, g, h) -> f1(a, b, c, d, e, f, g, h) [ b >= a ] (1, 1) start(a, b, c, d, e, f, g, h) -> f2(a, b, c, d, e, f, g, h) start location: start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [a, b, c, d, e]. We thus obtain the following problem: 2: T: (1, 1) start(a, b, c, d, e) -> f2(a, b, c, d, e) (?, 1) f2(a, b, c, d, e) -> f1(a, b, c, d, e) [ b >= a ] (?, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\ e >= a + 1 ] (?, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\ e >= a + 1 ] (?, 1) f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\ b = d ] (?, 1) f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ] (?, 1) f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ] (?, 1) f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ] (?, 1) f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ] (?, 1) f49(a, b, c, d, e) -> f49(a, b, c, d, e + 1) [ a >= e ] (?, 1) f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ] (?, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ] (?, 1) f27(a, b, c, d, e) -> f27(a, b, c, d, e + 1) [ a >= e ] (?, 1) f19(a, b, c, d, e) -> f19(a, b, c, d, e + 1) [ a >= e ] (?, 1) f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\ i >= k + 1 ] (?, 1) f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\ i >= j ] (?, 1) f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ] start location: start leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (1, 1) start(a, b, c, d, e) -> f2(a, b, c, d, e) (?, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\ e >= a + 1 ] (?, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\ e >= a + 1 ] (?, 1) f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\ b = d ] (?, 1) f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ] (?, 1) f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ] (?, 1) f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ] (?, 1) f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ] (?, 1) f49(a, b, c, d, e) -> f49(a, b, c, d, e + 1) [ a >= e ] (?, 1) f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ] (?, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ] (?, 1) f27(a, b, c, d, e) -> f27(a, b, c, d, e + 1) [ a >= e ] (?, 1) f19(a, b, c, d, e) -> f19(a, b, c, d, e + 1) [ a >= e ] (?, 1) f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\ i >= k + 1 ] (?, 1) f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\ i >= j ] (?, 1) f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ] start location: start leaf cost: 1 Testing for reachability in the complexity graph removes the following transitions from problem 3: f49(a, b, c, d, e) -> f49(a, b, c, d, e + 1) [ a >= e ] f27(a, b, c, d, e) -> f27(a, b, c, d, e + 1) [ a >= e ] f19(a, b, c, d, e) -> f19(a, b, c, d, e + 1) [ a >= e ] We thus obtain the following problem: 4: T: (?, 1) f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ] (?, 1) f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ] (?, 1) f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ] (?, 1) f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ] (?, 1) f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\ e >= a + 1 ] (?, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\ e >= a + 1 ] (?, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ] (?, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ] (?, 1) f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ] (?, 1) f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\ i >= j ] (?, 1) f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\ i >= k + 1 ] (?, 1) f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\ b = d ] (?, 1) f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ] (1, 1) start(a, b, c, d, e) -> f2(a, b, c, d, e) start location: start leaf cost: 1 A polynomial rank function with Pol(f49) = 6*V_1 - 6*V_2 - 5 Pol(f36) = 6*V_1 - 6*V_2 - 5 Pol(f43) = 6*V_1 - 6*V_2 - 5 Pol(f27) = 6*V_1 - 6*V_2 - 3 Pol(f34) = 6*V_1 - 6*V_2 - 4 Pol(f2) = 6*V_1 - 6*V_2 Pol(f19) = 6*V_1 - 6*V_2 - 2 Pol(f8) = 6*V_1 - 6*V_2 - 1 Pol(start) = 6*V_1 - 6*V_2 orients all transitions weakly and the transition f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ] strictly and produces the following problem: 5: T: (?, 1) f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ] (?, 1) f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ] (?, 1) f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ] (?, 1) f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ] (?, 1) f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\ e >= a + 1 ] (?, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\ e >= a + 1 ] (?, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ] (?, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ] (?, 1) f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ] (?, 1) f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\ i >= j ] (?, 1) f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\ i >= k + 1 ] (?, 1) f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\ b = d ] (6*a + 6*b, 1) f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ] (1, 1) start(a, b, c, d, e) -> f2(a, b, c, d, e) start location: start leaf cost: 1 A polynomial rank function with Pol(f8) = 5 Pol(f34) = 2 Pol(f19) = 4 Pol(f49) = 1 Pol(f36) = 1 Pol(f43) = 1 Pol(f2) = 0 Pol(f27) = 3 and size complexities S("start(a, b, c, d, e) -> f2(a, b, c, d, e)", 0-0) = a S("start(a, b, c, d, e) -> f2(a, b, c, d, e)", 0-1) = b S("start(a, b, c, d, e) -> f2(a, b, c, d, e)", 0-2) = c S("start(a, b, c, d, e) -> f2(a, b, c, d, e)", 0-3) = d S("start(a, b, c, d, e) -> f2(a, b, c, d, e)", 0-4) = e S("f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ]", 0-0) = a S("f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ]", 0-1) = ? S("f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ]", 0-2) = 0 S("f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ]", 0-3) = ? S("f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ]", 0-4) = ? S("f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\\ b = d ]", 0-0) = a S("f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\\ b = d ]", 0-1) = ? S("f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\\ b = d ]", 0-2) = ? S("f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\\ b = d ]", 0-3) = ? S("f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\\ b = d ]", 0-4) = ? S("f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\\ i >= k + 1 ]", 0-0) = a S("f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\\ i >= k + 1 ]", 0-1) = ? S("f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\\ i >= k + 1 ]", 0-2) = ? S("f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\\ i >= k + 1 ]", 0-3) = ? S("f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\\ i >= k + 1 ]", 0-4) = ? S("f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\\ i >= j ]", 0-0) = a S("f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\\ i >= j ]", 0-1) = ? S("f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\\ i >= j ]", 0-2) = ? S("f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\\ i >= j ]", 0-3) = ? S("f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\\ i >= j ]", 0-4) = ? S("f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ]", 0-0) = a S("f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ]", 0-1) = ? S("f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ]", 0-2) = 0 S("f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ]", 0-3) = ? S("f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ]", 0-4) = ? S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ]", 0-0) = a S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ]", 0-1) = ? S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ]", 0-2) = ? S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ]", 0-3) = ? S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ]", 0-4) = ? S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ]", 0-0) = a S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ]", 0-1) = ? S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ]", 0-2) = ? S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ]", 0-3) = ? S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ]", 0-4) = ? S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\\ e >= a + 1 ]", 0-0) = a S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\\ e >= a + 1 ]", 0-1) = ? S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\\ e >= a + 1 ]", 0-2) = ? S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\\ e >= a + 1 ]", 0-3) = ? S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\\ e >= a + 1 ]", 0-4) = ? S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\\ e >= a + 1 ]", 0-0) = a S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\\ e >= a + 1 ]", 0-1) = ? S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\\ e >= a + 1 ]", 0-2) = ? S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\\ e >= a + 1 ]", 0-3) = ? S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\\ e >= a + 1 ]", 0-4) = ? S("f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ]", 0-0) = a S("f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ]", 0-1) = ? S("f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ]", 0-2) = ? S("f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ]", 0-3) = ? S("f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ]", 0-4) = ? S("f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ]", 0-0) = a S("f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ]", 0-1) = ? S("f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ]", 0-2) = ? S("f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ]", 0-3) = ? S("f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ]", 0-4) = ? S("f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ]", 0-0) = a S("f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ]", 0-1) = ? S("f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ]", 0-2) = ? S("f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ]", 0-3) = ? S("f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ]", 0-4) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-0) = a S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-1) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-2) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-3) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-4) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-0) = a S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-1) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-2) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-3) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-4) = ? S("f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ]", 0-0) = a S("f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ]", 0-1) = ? S("f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ]", 0-2) = ? S("f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ]", 0-3) = ? S("f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ]", 0-4) = ? S("f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ]", 0-0) = a S("f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ]", 0-1) = ? S("f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ]", 0-2) = ? S("f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ]", 0-3) = ? S("f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ]", 0-4) = ? S("f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ]", 0-0) = a S("f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ]", 0-1) = ? S("f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ]", 0-2) = ? S("f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ]", 0-3) = ? S("f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ]", 0-4) = ? S("f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ]", 0-0) = a S("f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ]", 0-1) = ? S("f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ]", 0-2) = ? S("f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ]", 0-3) = ? S("f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ]", 0-4) = ? orients the transitions f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\ i >= k + 1 ] f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\ i >= j ] f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\ b = d ] f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\ e >= a + 1 ] f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\ e >= a + 1 ] f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ] f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ] f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ] f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ] f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ] f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ] f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ] f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ] f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ] f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ] weakly and the transitions f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\ b = d ] f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\ e >= a + 1 ] f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\ e >= a + 1 ] f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ] f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ] f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ] f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ] f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ] f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ] strictly and produces the following problem: 6: T: (?, 1) f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ] (?, 1) f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ] (?, 1) f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ] (30*a + 30*b, 1) f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ] (30*a + 30*b, 1) f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ] (30*a + 30*b, 1) f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\ e >= a + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\ e >= a + 1 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ] (?, 1) f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\ i >= j ] (?, 1) f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\ i >= k + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\ b = d ] (6*a + 6*b, 1) f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ] (1, 1) start(a, b, c, d, e) -> f2(a, b, c, d, e) start location: start leaf cost: 1 A polynomial rank function with Pol(f49) = 2*V_1 - 2*V_5 + 1 Pol(f36) = 2*V_1 - 2*V_5 + 1 Pol(f43) = 2*V_1 - 2*V_5 + 1 Pol(f27) = 2*V_1 - 2*V_5 + 1 Pol(f34) = 2*V_1 - 2*V_5 + 1 Pol(f2) = 2*V_1 - 2*V_5 + 1 Pol(f19) = 2*V_1 - 2*V_5 + 1 Pol(f8) = 2*V_1 - 2*V_5 + 1 Pol(start) = 2*V_1 - 2*V_5 + 1 orients all transitions weakly and the transitions f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\ i >= k + 1 ] f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\ i >= j ] f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ] strictly and produces the following problem: 7: T: (?, 1) f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ e >= a + 1 ] (2*a + 2*e + 1, 1) f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ a >= e ] (?, 1) f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ e >= a + 1 ] (30*a + 30*b, 1) f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ e >= a + 1 ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ a >= d ] (30*a + 30*b, 1) f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ d >= a + 1 ] (30*a + 30*b, 1) f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ e >= a + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ b >= d + 1 /\ e >= a + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ d >= b + 1 /\ e >= a + 1 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ 0 >= c + 1 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ c >= 1 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ c = 0 ] (2*a + 2*e + 1, 1) f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a >= e /\ i >= j ] (2*a + 2*e + 1, 1) f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a >= e /\ i >= k + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ e >= a + 1 /\ b = d ] (6*a + 6*b, 1) f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ] (1, 1) start(a, b, c, d, e) -> f2(a, b, c, d, e) start location: start leaf cost: 1 Applied AI with 'oct' on problem 7 to obtain the following invariants: For symbol f19: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f27: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f34: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f36: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f43: -X_4 + X_5 - 1 >= 0 /\ -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f49: -X_4 + X_5 - 1 >= 0 /\ -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f8: X_1 - X_2 - 1 >= 0 This yielded the following problem: 8: T: (1, 1) start(a, b, c, d, e) -> f2(a, b, c, d, e) (6*a + 6*b, 1) f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ a - b - 1 >= 0 /\ e >= a + 1 /\ b = d ] (2*a + 2*e + 1, 1) f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a - b - 1 >= 0 /\ a >= e /\ i >= k + 1 ] (2*a + 2*e + 1, 1) f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a - b - 1 >= 0 /\ a >= e /\ i >= j ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ c = 0 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ c >= 1 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ 0 >= c + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\ d >= b + 1 /\ e >= a + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\ b >= d + 1 /\ e >= a + 1 ] (30*a + 30*b, 1) f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] (30*a + 30*b, 1) f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ d >= a + 1 ] (?, 1) f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ a >= d ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (30*a + 30*b, 1) f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] (?, 1) f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] (2*a + 2*e + 1, 1) f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ a >= e ] (?, 1) f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] start location: start leaf cost: 1 Testing for unsatisfiable constraints removes the following transition from problem 8: f43(a, b, c, d, e) -> f43(a, b, c, d, e + 1) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ a >= e ] We thus obtain the following problem: 9: T: (1, 1) start(a, b, c, d, e) -> f2(a, b, c, d, e) (6*a + 6*b, 1) f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ a - b - 1 >= 0 /\ e >= a + 1 /\ b = d ] (2*a + 2*e + 1, 1) f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a - b - 1 >= 0 /\ a >= e /\ i >= k + 1 ] (2*a + 2*e + 1, 1) f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a - b - 1 >= 0 /\ a >= e /\ i >= j ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ c = 0 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ c >= 1 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ 0 >= c + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\ d >= b + 1 /\ e >= a + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\ b >= d + 1 /\ e >= a + 1 ] (30*a + 30*b, 1) f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] (30*a + 30*b, 1) f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ d >= a + 1 ] (?, 1) f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ a >= d ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (?, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (30*a + 30*b, 1) f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] (?, 1) f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] (?, 1) f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] start location: start leaf cost: 1 A polynomial rank function with Pol(f49) = 3*V_1 - 3*V_4 + 1 Pol(f36) = 3*V_1 - 3*V_4 + 3 Pol(f43) = 3*V_1 - 3*V_4 + 2 and size complexities S("f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -d + e - 1 >= 0 /\\ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - d >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-0) = a S("f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -d + e - 1 >= 0 /\\ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - d >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-1) = 61*a + 61*b S("f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -d + e - 1 >= 0 /\\ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - d >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-2) = ? S("f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -d + e - 1 >= 0 /\\ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - d >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-3) = ? S("f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -d + e - 1 >= 0 /\\ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - d >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-4) = 5*a + 5*e + 50 S("f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ -d + e - 1 >= 0 /\\ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - d >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-0) = a S("f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ -d + e - 1 >= 0 /\\ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - d >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-1) = 61*a + 61*b S("f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ -d + e - 1 >= 0 /\\ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - d >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-2) = ? S("f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ -d + e - 1 >= 0 /\\ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - d >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-3) = ? S("f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ -d + e - 1 >= 0 /\\ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - d >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-4) = 5*a + 5*e + 50 S("f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-0) = a S("f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-1) = 61*a + 61*b S("f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-2) = ? S("f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-3) = 61*a + 61*b + 61*e + 42229815050 S("f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-4) = 5*a + 5*e + 50 S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ 0 >= i + 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-0) = a S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ 0 >= i + 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-1) = 61*a + 61*b S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ 0 >= i + 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-2) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ 0 >= i + 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-3) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ 0 >= i + 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-4) = 5*a + 5*e + 50 S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ i >= 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-0) = a S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ i >= 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-1) = 61*a + 61*b S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ i >= 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-2) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ i >= 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-3) = ? S("f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ i >= 1 /\\ a >= d /\\ i >= c*k /\\ c*k + k >= i + 1 /\\ k >= j /\\ i >= c*l /\\ c*l + l >= i + 1 /\\ j >= l ]", 0-4) = 5*a + 5*e + 50 S("f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ a >= d ]", 0-0) = a S("f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ a >= d ]", 0-1) = 61*a + 61*b S("f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ a >= d ]", 0-2) = ? S("f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ a >= d ]", 0-3) = ? S("f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ a >= d ]", 0-4) = 5*a + 5*e + 50 S("f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ d >= a + 1 ]", 0-0) = a S("f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ d >= a + 1 ]", 0-1) = 61*a + 61*b S("f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ d >= a + 1 ]", 0-2) = ? S("f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ d >= a + 1 ]", 0-3) = ? S("f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ d >= a + 1 ]", 0-4) = 5*a + 5*e + 50 S("f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-0) = a S("f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-1) = 61*a + 61*b S("f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-2) = ? S("f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-3) = 61*a + 61*b + 61*e + 692292050 S("f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ e >= a + 1 ]", 0-4) = 5*a + 5*e + 50 S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\\ b >= d + 1 /\\ e >= a + 1 ]", 0-0) = a S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\\ b >= d + 1 /\\ e >= a + 1 ]", 0-1) = 61*a + 61*b S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\\ b >= d + 1 /\\ e >= a + 1 ]", 0-2) = ? S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\\ b >= d + 1 /\\ e >= a + 1 ]", 0-3) = 61*a + 61*b + 61*e + 11349050 S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\\ b >= d + 1 /\\ e >= a + 1 ]", 0-4) = 5*a + 5*e + 50 S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\\ d >= b + 1 /\\ e >= a + 1 ]", 0-0) = a S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\\ d >= b + 1 /\\ e >= a + 1 ]", 0-1) = 61*a + 61*b S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\\ d >= b + 1 /\\ e >= a + 1 ]", 0-2) = ? S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\\ d >= b + 1 /\\ e >= a + 1 ]", 0-3) = 61*a + 61*b + 61*e + 11349050 S("f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\\ d >= b + 1 /\\ e >= a + 1 ]", 0-4) = 5*a + 5*e + 50 S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ 0 >= c + 1 ]", 0-0) = a S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ 0 >= c + 1 ]", 0-1) = 61*a + 61*b S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ 0 >= c + 1 ]", 0-2) = ? S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ 0 >= c + 1 ]", 0-3) = 61*a + 61*b + 61*e + 2576018718050 S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ 0 >= c + 1 ]", 0-4) = 5*a + 5*e + 50 S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ c >= 1 ]", 0-0) = a S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ c >= 1 ]", 0-1) = 61*a + 61*b S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ c >= 1 ]", 0-2) = ? S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ c >= 1 ]", 0-3) = 61*a + 61*b + 61*e + 2576018718050 S("f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ c >= 1 ]", 0-4) = 5*a + 5*e + 50 S("f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ c = 0 ]", 0-0) = a S("f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ c = 0 ]", 0-1) = 61*a + 61*b S("f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ c = 0 ]", 0-2) = 0 S("f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ c = 0 ]", 0-3) = 61*a + 61*b + 61*e + 2576018718050 S("f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ -b + e - 2 >= 0 /\\ -a + e - 1 >= 0 /\\ a - b - 1 >= 0 /\\ c = 0 ]", 0-4) = 5*a + 5*e + 50 S("f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a - b - 1 >= 0 /\\ a >= e /\\ i >= j ]", 0-0) = a S("f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a - b - 1 >= 0 /\\ a >= e /\\ i >= j ]", 0-1) = 61*a + 61*b S("f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a - b - 1 >= 0 /\\ a >= e /\\ i >= j ]", 0-2) = ? S("f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a - b - 1 >= 0 /\\ a >= e /\\ i >= j ]", 0-3) = 61*a + 61*b + 61*e + 186050 S("f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a - b - 1 >= 0 /\\ a >= e /\\ i >= j ]", 0-4) = 5*a + 5*e + 50 S("f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a - b - 1 >= 0 /\\ a >= e /\\ i >= k + 1 ]", 0-0) = a S("f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a - b - 1 >= 0 /\\ a >= e /\\ i >= k + 1 ]", 0-1) = 61*a + 61*b S("f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a - b - 1 >= 0 /\\ a >= e /\\ i >= k + 1 ]", 0-2) = ? S("f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a - b - 1 >= 0 /\\ a >= e /\\ i >= k + 1 ]", 0-3) = 5*a + 5*e + 250 S("f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a - b - 1 >= 0 /\\ a >= e /\\ i >= k + 1 ]", 0-4) = 5*a + 5*e + 50 S("f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ a - b - 1 >= 0 /\\ e >= a + 1 /\\ b = d ]", 0-0) = a S("f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ a - b - 1 >= 0 /\\ e >= a + 1 /\\ b = d ]", 0-1) = 61*a + 61*b S("f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ a - b - 1 >= 0 /\\ e >= a + 1 /\\ b = d ]", 0-2) = ? S("f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ a - b - 1 >= 0 /\\ e >= a + 1 /\\ b = d ]", 0-3) = 61*a + 61*b S("f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ a - b - 1 >= 0 /\\ e >= a + 1 /\\ b = d ]", 0-4) = 5*a + 5*e + 50 S("f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ]", 0-0) = a S("f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ]", 0-1) = 61*a + 61*b S("f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ]", 0-2) = 0 S("f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ]", 0-3) = 61*a + 61*b S("f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ]", 0-4) = 5*a + 5*e + 50 S("start(a, b, c, d, e) -> f2(a, b, c, d, e)", 0-0) = a S("start(a, b, c, d, e) -> f2(a, b, c, d, e)", 0-1) = b S("start(a, b, c, d, e) -> f2(a, b, c, d, e)", 0-2) = c S("start(a, b, c, d, e) -> f2(a, b, c, d, e)", 0-3) = d S("start(a, b, c, d, e) -> f2(a, b, c, d, e)", 0-4) = e orients the transitions f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ a >= d ] weakly and the transitions f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ a >= d ] strictly and produces the following problem: 10: T: (1, 1) start(a, b, c, d, e) -> f2(a, b, c, d, e) (6*a + 6*b, 1) f2(a, b, c, d, e) -> f8(a, b, 0, b, e) [ a >= b + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f34(a, b, c, b, e) [ a - b - 1 >= 0 /\ e >= a + 1 /\ b = d ] (2*a + 2*e + 1, 1) f8(a, b, c, d, e) -> f8(a, b, j, e, e + 1) [ a - b - 1 >= 0 /\ a >= e /\ i >= k + 1 ] (2*a + 2*e + 1, 1) f8(a, b, c, d, e) -> f8(a, b, c, d, e + 1) [ a - b - 1 >= 0 /\ a >= e /\ i >= j ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f2(a, b + 1, 0, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ c = 0 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ c >= 1 ] (30*a + 30*b, 1) f34(a, b, c, d, e) -> f36(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ 0 >= c + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\ d >= b + 1 /\ e >= a + 1 ] (30*a + 30*b, 1) f8(a, b, c, d, e) -> f19(a, b, c, d, e) [ a - b - 1 >= 0 /\ b >= d + 1 /\ e >= a + 1 ] (30*a + 30*b, 1) f19(a, b, c, d, e) -> f27(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] (30*a + 30*b, 1) f36(a, b, c, d, e) -> f2(a, b + 1, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ d >= a + 1 ] (11160*a^2 + 22140*a*b + 10980*b^2 + 10980*a*e + 10980*b*e + 463683369249180*a + 463683369249180*b, 1) f36(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ a >= d ] (11160*a^2 + 22140*a*b + 10980*b^2 + 10980*a*e + 10980*b*e + 463683369249180*a + 463683369249180*b, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ i >= 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (11160*a^2 + 22140*a*b + 10980*b^2 + 10980*a*e + 10980*b*e + 463683369249180*a + 463683369249180*b, 1) f36(a, b, c, d, e) -> f43(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ 0 >= i + 1 /\ a >= d /\ i >= c*k /\ c*k + k >= i + 1 /\ k >= j /\ i >= c*l /\ c*l + l >= i + 1 /\ j >= l ] (30*a + 30*b, 1) f27(a, b, c, d, e) -> f34(a, b, c, d, e) [ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] (11160*a^2 + 22140*a*b + 10980*b^2 + 10980*a*e + 10980*b*e + 463683369249180*a + 463683369249180*b, 1) f43(a, b, c, d, e) -> f49(a, b, c, d, e) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] (11160*a^2 + 22140*a*b + 10980*b^2 + 10980*a*e + 10980*b*e + 463683369249180*a + 463683369249180*b, 1) f49(a, b, c, d, e) -> f36(a, b, c, d + 1, e) [ -d + e - 1 >= 0 /\ -b + e - 2 >= 0 /\ -a + e - 1 >= 0 /\ a - d >= 0 /\ a - b - 1 >= 0 /\ e >= a + 1 ] start location: start leaf cost: 1 Complexity upper bound 2318416846246180*a + 2318416846246176*b + 4*e + 55800*a^2 + 110700*a*b + 54900*b^2 + 54900*a*e + 54900*b*e + 4 Time: 1.495 sec (SMT: 1.351 sec)