YES(?, 28*a + 10) Initial complexity problem: 1: T: (1, 1) evalspeedpldi2start(a, b, c) -> evalspeedpldi2entryin(a, b, c) (?, 1) evalspeedpldi2entryin(a, b, c) -> evalspeedpldi2bb5in(b, 0, a) [ a >= 0 /\ b >= 1 ] (?, 1) evalspeedpldi2entryin(a, b, c) -> evalspeedpldi2returnin(a, b, c) [ 0 >= a + 1 ] (?, 1) evalspeedpldi2entryin(a, b, c) -> evalspeedpldi2returnin(a, b, c) [ 0 >= b ] (?, 1) evalspeedpldi2bb5in(a, b, c) -> evalspeedpldi2bb2in(a, b, c) [ c >= 1 ] (?, 1) evalspeedpldi2bb5in(a, b, c) -> evalspeedpldi2returnin(a, b, c) [ 0 >= c ] (?, 1) evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb3in(a, b, c) [ a >= b + 1 ] (?, 1) evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb5in(a, 0, c) [ b >= a ] (?, 1) evalspeedpldi2bb3in(a, b, c) -> evalspeedpldi2bb5in(a, b + 1, c - 1) (?, 1) evalspeedpldi2returnin(a, b, c) -> evalspeedpldi2stop(a, b, c) start location: evalspeedpldi2start leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) evalspeedpldi2start(a, b, c) -> evalspeedpldi2entryin(a, b, c) (?, 1) evalspeedpldi2entryin(a, b, c) -> evalspeedpldi2bb5in(b, 0, a) [ a >= 0 /\ b >= 1 ] (?, 1) evalspeedpldi2bb5in(a, b, c) -> evalspeedpldi2bb2in(a, b, c) [ c >= 1 ] (?, 1) evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb3in(a, b, c) [ a >= b + 1 ] (?, 1) evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb5in(a, 0, c) [ b >= a ] (?, 1) evalspeedpldi2bb3in(a, b, c) -> evalspeedpldi2bb5in(a, b + 1, c - 1) start location: evalspeedpldi2start leaf cost: 4 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) evalspeedpldi2start(a, b, c) -> evalspeedpldi2entryin(a, b, c) (1, 1) evalspeedpldi2entryin(a, b, c) -> evalspeedpldi2bb5in(b, 0, a) [ a >= 0 /\ b >= 1 ] (?, 1) evalspeedpldi2bb5in(a, b, c) -> evalspeedpldi2bb2in(a, b, c) [ c >= 1 ] (?, 1) evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb3in(a, b, c) [ a >= b + 1 ] (?, 1) evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb5in(a, 0, c) [ b >= a ] (?, 1) evalspeedpldi2bb3in(a, b, c) -> evalspeedpldi2bb5in(a, b + 1, c - 1) start location: evalspeedpldi2start leaf cost: 4 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalspeedpldi2bb2in: X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalspeedpldi2bb3in: X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalspeedpldi2bb5in: X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 This yielded the following problem: 4: T: (?, 1) evalspeedpldi2bb3in(a, b, c) -> evalspeedpldi2bb5in(a, b + 1, c - 1) [ c - 1 >= 0 /\ b + c - 1 >= 0 /\ a + c - 2 >= 0 /\ a - b - 1 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 ] (?, 1) evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb5in(a, 0, c) [ c - 1 >= 0 /\ b + c - 1 >= 0 /\ a + c - 2 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 /\ b >= a ] (?, 1) evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb3in(a, b, c) [ c - 1 >= 0 /\ b + c - 1 >= 0 /\ a + c - 2 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 /\ a >= b + 1 ] (?, 1) evalspeedpldi2bb5in(a, b, c) -> evalspeedpldi2bb2in(a, b, c) [ c >= 0 /\ b + c >= 0 /\ a + c - 1 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 /\ c >= 1 ] (1, 1) evalspeedpldi2entryin(a, b, c) -> evalspeedpldi2bb5in(b, 0, a) [ a >= 0 /\ b >= 1 ] (1, 1) evalspeedpldi2start(a, b, c) -> evalspeedpldi2entryin(a, b, c) start location: evalspeedpldi2start leaf cost: 4 A polynomial rank function with Pol(evalspeedpldi2bb3in) = 4*V_2 + 7*V_3 - 1 Pol(evalspeedpldi2bb5in) = 4*V_2 + 7*V_3 + 1 Pol(evalspeedpldi2bb2in) = 4*V_2 + 7*V_3 Pol(evalspeedpldi2entryin) = 7*V_1 + 1 Pol(evalspeedpldi2start) = 7*V_1 + 1 orients all transitions weakly and the transitions evalspeedpldi2bb5in(a, b, c) -> evalspeedpldi2bb2in(a, b, c) [ c >= 0 /\ b + c >= 0 /\ a + c - 1 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 /\ c >= 1 ] evalspeedpldi2bb3in(a, b, c) -> evalspeedpldi2bb5in(a, b + 1, c - 1) [ c - 1 >= 0 /\ b + c - 1 >= 0 /\ a + c - 2 >= 0 /\ a - b - 1 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 ] evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb5in(a, 0, c) [ c - 1 >= 0 /\ b + c - 1 >= 0 /\ a + c - 2 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 /\ b >= a ] evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb3in(a, b, c) [ c - 1 >= 0 /\ b + c - 1 >= 0 /\ a + c - 2 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 /\ a >= b + 1 ] strictly and produces the following problem: 5: T: (7*a + 1, 1) evalspeedpldi2bb3in(a, b, c) -> evalspeedpldi2bb5in(a, b + 1, c - 1) [ c - 1 >= 0 /\ b + c - 1 >= 0 /\ a + c - 2 >= 0 /\ a - b - 1 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 ] (7*a + 1, 1) evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb5in(a, 0, c) [ c - 1 >= 0 /\ b + c - 1 >= 0 /\ a + c - 2 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 /\ b >= a ] (7*a + 1, 1) evalspeedpldi2bb2in(a, b, c) -> evalspeedpldi2bb3in(a, b, c) [ c - 1 >= 0 /\ b + c - 1 >= 0 /\ a + c - 2 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 /\ a >= b + 1 ] (7*a + 1, 1) evalspeedpldi2bb5in(a, b, c) -> evalspeedpldi2bb2in(a, b, c) [ c >= 0 /\ b + c >= 0 /\ a + c - 1 >= 0 /\ b >= 0 /\ a + b - 1 >= 0 /\ a - 1 >= 0 /\ c >= 1 ] (1, 1) evalspeedpldi2entryin(a, b, c) -> evalspeedpldi2bb5in(b, 0, a) [ a >= 0 /\ b >= 1 ] (1, 1) evalspeedpldi2start(a, b, c) -> evalspeedpldi2entryin(a, b, c) start location: evalspeedpldi2start leaf cost: 4 Complexity upper bound 28*a + 10 Time: 0.374 sec (SMT: 0.353 sec)