YES(?, 248*a + 45*c + 8960) Initial complexity problem: 1: T: (?, 1) start(a, b, c, d) -> stop(a, b, c, d) [ a >= 30 /\ b = c /\ d = a ] (?, 1) start(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ c >= a /\ 29 >= a /\ b = c /\ d = a ] (?, 1) start(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ a >= c + 1 /\ c >= 6 /\ 29 >= a /\ b = c /\ d = a ] (?, 1) start(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ a >= c + 1 /\ 5 >= c /\ 29 >= a /\ b = c /\ d = a ] (?, 1) lbl171(a, b, c, d) -> stop(a, b, c, d) [ d >= 30 /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (?, 1) lbl171(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (?, 1) lbl171(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (?, 1) lbl171(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (?, 1) lbl151(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (?, 1) lbl151(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (?, 1) lbl151(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (1, 1) start0(a, b, c, d) -> start(a, c, c, a) start location: start0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (?, 1) start(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ c >= a /\ 29 >= a /\ b = c /\ d = a ] (?, 1) start(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ a >= c + 1 /\ c >= 6 /\ 29 >= a /\ b = c /\ d = a ] (?, 1) start(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ a >= c + 1 /\ 5 >= c /\ 29 >= a /\ b = c /\ d = a ] (?, 1) lbl171(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (?, 1) lbl171(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (?, 1) lbl171(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (?, 1) lbl151(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (?, 1) lbl151(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (?, 1) lbl151(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (1, 1) start0(a, b, c, d) -> start(a, c, c, a) start location: start0 leaf cost: 2 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) start(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ c >= a /\ 29 >= a /\ b = c /\ d = a ] (1, 1) start(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ a >= c + 1 /\ c >= 6 /\ 29 >= a /\ b = c /\ d = a ] (1, 1) start(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ a >= c + 1 /\ 5 >= c /\ 29 >= a /\ b = c /\ d = a ] (?, 1) lbl171(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (?, 1) lbl171(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (?, 1) lbl171(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (?, 1) lbl151(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (?, 1) lbl151(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (?, 1) lbl151(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (1, 1) start0(a, b, c, d) -> start(a, c, c, a) start location: start0 leaf cost: 2 A polynomial rank function with Pol(start) = -40*V_1 - V_2 - 8*V_3 - 7*V_4 + 1720 Pol(lbl171) = -40*V_1 - V_2 - 8*V_3 - 7*V_4 + 1724 Pol(lbl151) = -40*V_1 - V_2 - 8*V_3 - 7*V_4 + 1721 Pol(start0) = -47*V_1 - 9*V_3 + 1720 orients all transitions weakly and the transitions lbl171(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] lbl171(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] lbl151(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] lbl151(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] lbl151(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] strictly and produces the following problem: 4: T: (1, 1) start(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ c >= a /\ 29 >= a /\ b = c /\ d = a ] (1, 1) start(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ a >= c + 1 /\ c >= 6 /\ 29 >= a /\ b = c /\ d = a ] (1, 1) start(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ a >= c + 1 /\ 5 >= c /\ 29 >= a /\ b = c /\ d = a ] (?, 1) lbl171(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (47*a + 9*c + 1720, 1) lbl171(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (47*a + 9*c + 1720, 1) lbl171(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (47*a + 9*c + 1720, 1) lbl151(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (47*a + 9*c + 1720, 1) lbl151(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (47*a + 9*c + 1720, 1) lbl151(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (1, 1) start0(a, b, c, d) -> start(a, c, c, a) start location: start0 leaf cost: 2 A polynomial rank function with Pol(start) = -13*V_1 - V_2 + V_3 + 354 Pol(lbl171) = -7*V_1 - V_2 + V_3 - 6*V_4 + 354 Pol(lbl151) = -7*V_1 - V_2 + V_3 - 6*V_4 + 362 Pol(start0) = -13*V_1 + 354 orients all transitions weakly and the transition lbl171(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] strictly and produces the following problem: 5: T: (1, 1) start(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ c >= a /\ 29 >= a /\ b = c /\ d = a ] (1, 1) start(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ a >= c + 1 /\ c >= 6 /\ 29 >= a /\ b = c /\ d = a ] (1, 1) start(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ a >= c + 1 /\ 5 >= c /\ 29 >= a /\ b = c /\ d = a ] (13*a + 354, 1) lbl171(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (47*a + 9*c + 1720, 1) lbl171(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (47*a + 9*c + 1720, 1) lbl171(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 29 >= d /\ 29 >= a /\ 5*d + b >= 5*a + c /\ 7*d + c >= b + 7*a + 24 /\ 7*b + 1674 >= 19*d + 35*a + 7*c /\ b + 12 >= d ] (47*a + 9*c + 1720, 1) lbl151(a, b, c, d) -> lbl171(a, b - 10, c, d + 2) [ b >= d /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (47*a + 9*c + 1720, 1) lbl151(a, b, c, d) -> lbl151(a, b + 7, c, d + 1) [ d >= b + 1 /\ b >= 6 /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (47*a + 9*c + 1720, 1) lbl151(a, b, c, d) -> lbl151(a, b + 2, c, d + 1) [ d >= b + 1 /\ 5 >= b /\ 6*d >= 5*a + c + 7 /\ 5*d + b >= 5*a + c + 7 /\ d >= a + 1 /\ 29 >= a /\ b + 203 >= 2*d + 5*a + c /\ 2*b + 1561 >= 14*d + 35*a + 7*c /\ 140*d + 23*b >= 140*a + 28*c + 161 /\ 23*b + 5719 >= 56*d + 140*a + 28*c /\ d + 5 >= b /\ 7*d + c >= b + 7*a ] (1, 1) start0(a, b, c, d) -> start(a, c, c, a) start location: start0 leaf cost: 2 Complexity upper bound 248*a + 45*c + 8960 Time: 1.197 sec (SMT: 1.148 sec)