7.95/3.58 WORST_CASE(Omega(n^1), O(n^2)) 7.95/3.59 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 7.95/3.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.95/3.59 7.95/3.59 7.95/3.59 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). 7.95/3.59 7.95/3.59 (0) CpxIntTrs 7.95/3.59 (1) Koat Proof [FINISHED, 1508 ms] 7.95/3.59 (2) BOUNDS(1, n^2) 7.95/3.59 (3) Loat Proof [FINISHED, 921 ms] 7.95/3.59 (4) BOUNDS(n^1, INF) 7.95/3.59 7.95/3.59 7.95/3.59 ---------------------------------------- 7.95/3.59 7.95/3.59 (0) 7.95/3.59 Obligation: 7.95/3.59 Complexity Int TRS consisting of the following rules: 7.95/3.59 eval_start_start(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb0_in(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_bb0_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_0(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_0(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_1(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_1(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_2(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_2(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_3(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_3(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb1_in(v_dir, v_i_0, v_m, v_n)) :|: 0 < v_m 7.95/3.59 eval_start_3(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb6_in(v_dir, v_i_0, v_m, v_n)) :|: 0 >= v_m 7.95/3.59 eval_start_bb1_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb2_in(v_dir, v_m, v_m, v_n)) :|: v_m < v_n 7.95/3.59 eval_start_bb1_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb5_in(v_dir, v_i_0, v_m, v_n)) :|: v_m >= v_n 7.95/3.59 eval_start_bb2_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb3_in(v_dir, v_i_0, v_m, v_n)) :|: 0 < v_i_0 && v_i_0 < v_n 7.95/3.59 eval_start_bb2_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb4_in(v_dir, v_i_0, v_m, v_n)) :|: 0 >= v_i_0 7.95/3.59 eval_start_bb2_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb4_in(v_dir, v_i_0, v_m, v_n)) :|: v_i_0 >= v_n 7.95/3.59 eval_start_bb3_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb2_in(v_dir, v_i_0 + 1, v_m, v_n)) :|: v_dir >= 1 && v_dir <= 1 7.95/3.59 eval_start_bb3_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb2_in(v_dir, v_i_0 - 1, v_m, v_n)) :|: v_dir < 1 7.95/3.59 eval_start_bb3_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb2_in(v_dir, v_i_0 - 1, v_m, v_n)) :|: v_dir > 1 7.95/3.59 eval_start_bb4_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_stop(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_bb5_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_8(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_8(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_9(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_9(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_stop(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_bb6_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_10(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_10(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_11(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 eval_start_11(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_stop(v_dir, v_i_0, v_m, v_n)) :|: TRUE 7.95/3.59 7.95/3.59 The start-symbols are:[eval_start_start_4] 7.95/3.59 7.95/3.59 7.95/3.59 ---------------------------------------- 7.95/3.59 7.95/3.59 (1) Koat Proof (FINISHED) 7.95/3.59 YES(?, 10*ar_0 + 4*ar_1 + 4*ar_0*ar_1 + 4*ar_0^2 + 26) 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 Initial complexity problem: 7.95/3.59 7.95/3.59 1: T: 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 Repeatedly propagating knowledge in problem 1 produces the following problem: 7.95/3.59 7.95/3.59 2: T: 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 A polynomial rank function with 7.95/3.59 7.95/3.59 Pol(evalstartstart) = 2 7.95/3.59 7.95/3.59 Pol(evalstartbb0in) = 2 7.95/3.59 7.95/3.59 Pol(evalstart0) = 2 7.95/3.59 7.95/3.59 Pol(evalstart1) = 2 7.95/3.59 7.95/3.59 Pol(evalstart2) = 2 7.95/3.59 7.95/3.59 Pol(evalstart3) = 2 7.95/3.59 7.95/3.59 Pol(evalstartbb1in) = 2 7.95/3.59 7.95/3.59 Pol(evalstartbb6in) = 0 7.95/3.59 7.95/3.59 Pol(evalstartbb2in) = 2 7.95/3.59 7.95/3.59 Pol(evalstartbb5in) = 0 7.95/3.59 7.95/3.59 Pol(evalstartbb3in) = 2 7.95/3.59 7.95/3.59 Pol(evalstartbb4in) = 1 7.95/3.59 7.95/3.59 Pol(evalstartstop) = 0 7.95/3.59 7.95/3.59 Pol(evalstart8) = 0 7.95/3.59 7.95/3.59 Pol(evalstart9) = 0 7.95/3.59 7.95/3.59 Pol(evalstart10) = 0 7.95/3.59 7.95/3.59 Pol(evalstart11) = 0 7.95/3.59 7.95/3.59 Pol(koat_start) = 2 7.95/3.59 7.95/3.59 orients all transitions weakly and the transitions 7.95/3.59 7.95/3.59 evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 strictly and produces the following problem: 7.95/3.59 7.95/3.59 3: T: 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 Applied AI with 'oct' on problem 3 to obtain the following invariants: 7.95/3.59 7.95/3.59 For symbol evalstart10: -X_1 >= 0 7.95/3.59 7.95/3.59 For symbol evalstart11: -X_1 >= 0 7.95/3.59 7.95/3.59 For symbol evalstart8: X_1 - X_2 >= 0 /\ X_1 - 1 >= 0 7.95/3.59 7.95/3.59 For symbol evalstart9: X_1 - X_2 >= 0 /\ X_1 - 1 >= 0 7.95/3.59 7.95/3.59 For symbol evalstartbb1in: X_1 - 1 >= 0 7.95/3.59 7.95/3.59 For symbol evalstartbb2in: X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 7.95/3.59 7.95/3.59 For symbol evalstartbb3in: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 7.95/3.59 7.95/3.59 For symbol evalstartbb4in: X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 7.95/3.59 7.95/3.59 For symbol evalstartbb5in: X_1 - X_2 >= 0 /\ X_1 - 1 >= 0 7.95/3.59 7.95/3.59 For symbol evalstartbb6in: -X_1 >= 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 This yielded the following problem: 7.95/3.59 7.95/3.59 4: T: 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained: 7.95/3.59 7.95/3.59 koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 5: T: 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 Testing for reachability in the complexity graph removes the following transition from problem 5: 7.95/3.59 7.95/3.59 evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 6: T: 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 By chaining the transition evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] with all transitions in problem 6, the following new transition is obtained: 7.95/3.59 7.95/3.59 evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 7: T: 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 By chaining the transition evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] with all transitions in problem 7, the following new transition is obtained: 7.95/3.59 7.95/3.59 evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 8: T: 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 Testing for reachability in the complexity graph removes the following transition from problem 8: 7.95/3.59 7.95/3.59 evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 9: T: 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 By chaining the transition evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] with all transitions in problem 9, the following new transition is obtained: 7.95/3.59 7.95/3.59 evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 10: T: 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 2) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 Testing for reachability in the complexity graph removes the following transition from problem 10: 7.95/3.59 7.95/3.59 evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 11: T: 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 2) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 By chaining the transition evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] with all transitions in problem 11, the following new transition is obtained: 7.95/3.59 7.95/3.59 evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 12: T: 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 3) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 2) evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 Testing for reachability in the complexity graph removes the following transition from problem 12: 7.95/3.59 7.95/3.59 evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 13: T: 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 3) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 By chaining the transition evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart11(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] with all transitions in problem 13, the following new transition is obtained: 7.95/3.59 7.95/3.59 evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 14: T: 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 2) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 3) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 Testing for reachability in the complexity graph removes the following transition from problem 14: 7.95/3.59 7.95/3.59 evalstart11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 15: T: 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.59 7.95/3.59 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 3) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 2) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.59 7.95/3.59 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.59 7.95/3.59 start location: koat_start 7.95/3.59 7.95/3.59 leaf cost: 0 7.95/3.59 7.95/3.59 7.95/3.59 7.95/3.59 By chaining the transition evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] with all transitions in problem 15, the following new transition is obtained: 7.95/3.59 7.95/3.59 evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.59 7.95/3.59 We thus obtain the following problem: 7.95/3.59 7.95/3.59 16: T: 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 By chaining the transition evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] with all transitions in problem 16, the following new transition is obtained: 7.95/3.60 7.95/3.60 evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 17: T: 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Testing for reachability in the complexity graph removes the following transition from problem 17: 7.95/3.60 7.95/3.60 evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 - 1 >= 0 ] 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 18: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 By chaining the transition evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] with all transitions in problem 18, the following new transition is obtained: 7.95/3.60 7.95/3.60 evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 19: T: 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Testing for reachability in the complexity graph removes the following transition from problem 19: 7.95/3.60 7.95/3.60 evalstart10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 20: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 By chaining the transition evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] with all transitions in problem 20, the following new transition is obtained: 7.95/3.60 7.95/3.60 evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 21: T: 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Testing for reachability in the complexity graph removes the following transition from problem 21: 7.95/3.60 7.95/3.60 evalstartbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 22: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 By chaining the transition evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3)) with all transitions in problem 22, the following new transition is obtained: 7.95/3.60 7.95/3.60 evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 23: T: 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Testing for reachability in the complexity graph removes the following transition from problem 23: 7.95/3.60 7.95/3.60 evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 24: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 By chaining the transition evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3)) with all transitions in problem 24, the following new transition is obtained: 7.95/3.60 7.95/3.60 evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 25: T: 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Testing for reachability in the complexity graph removes the following transition from problem 25: 7.95/3.60 7.95/3.60 evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 26: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 By chaining the transition evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3)) with all transitions in problem 26, the following new transition is obtained: 7.95/3.60 7.95/3.60 evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 27: T: 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Testing for reachability in the complexity graph removes the following transition from problem 27: 7.95/3.60 7.95/3.60 evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 28: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] with all transitions in problem 28, the following new transition is obtained: 7.95/3.60 7.95/3.60 koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 29: T: 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 5) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Testing for reachability in the complexity graph removes the following transition from problem 29: 7.95/3.60 7.95/3.60 evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 30: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 5) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 By chaining the transition evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] with all transitions in problem 30, the following new transitions are obtained: 7.95/3.60 7.95/3.60 evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 7.95/3.60 7.95/3.60 evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 31: T: 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 3) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 2) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 5) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Testing for reachability in the complexity graph removes the following transition from problem 31: 7.95/3.60 7.95/3.60 evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 7.95/3.60 7.95/3.60 We thus obtain the following problem: 7.95/3.60 7.95/3.60 32: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 2) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 3) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 5) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 A polynomial rank function with 7.95/3.60 7.95/3.60 Pol(evalstartbb2in) = 1 7.95/3.60 7.95/3.60 Pol(evalstartstop) = 0 7.95/3.60 7.95/3.60 Pol(evalstartbb3in) = 1 7.95/3.60 7.95/3.60 Pol(evalstartbb1in) = 1 7.95/3.60 7.95/3.60 Pol(evalstart3) = 1 7.95/3.60 7.95/3.60 Pol(koat_start) = 1 7.95/3.60 7.95/3.60 orients all transitions weakly and the transition 7.95/3.60 7.95/3.60 evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 7.95/3.60 7.95/3.60 strictly and produces the following problem: 7.95/3.60 7.95/3.60 33: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 2) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 5) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 A polynomial rank function with 7.95/3.60 7.95/3.60 Pol(evalstartbb3in) = 2*V_3 - 1 7.95/3.60 7.95/3.60 Pol(evalstartbb2in) = 2*V_3 7.95/3.60 7.95/3.60 and size complexities 7.95/3.60 7.95/3.60 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 7.95/3.60 7.95/3.60 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-2) = ar_2 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\\ -ar_0 >= 0 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\\ -ar_0 >= 0 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\\ -ar_0 >= 0 ]", 0-2) = ar_2 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\\ -ar_0 >= 0 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-2) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 /\\ ar_0 - ar_1 >= 0 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 /\\ ar_0 - ar_1 >= 0 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 /\\ ar_0 - ar_1 >= 0 ]", 0-2) = ar_2 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 /\\ ar_0 - ar_1 >= 0 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-2) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-2) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-2) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-3) = 1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-2) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-3) = 1 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-2) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 orients the transitions 7.95/3.60 7.95/3.60 evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 weakly and the transitions 7.95/3.60 7.95/3.60 evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 strictly and produces the following problem: 7.95/3.60 7.95/3.60 34: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: 2*ar_0 + 1, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: ?, Cost: 2) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2*ar_0 + 1, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: 2*ar_0 + 1, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 5) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 A polynomial rank function with 7.95/3.60 7.95/3.60 Pol(evalstartbb3in) = V_2 - V_3 7.95/3.60 7.95/3.60 and size complexities 7.95/3.60 7.95/3.60 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 7.95/3.60 7.95/3.60 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-2) = ar_2 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\\ -ar_0 >= 0 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\\ -ar_0 >= 0 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\\ -ar_0 >= 0 ]", 0-2) = ar_2 7.95/3.60 7.95/3.60 S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\\ -ar_0 >= 0 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-2) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 1 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 /\\ ar_0 - ar_1 >= 0 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 /\\ ar_0 - ar_1 >= 0 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 /\\ ar_0 - ar_1 >= 0 ]", 0-2) = ar_2 7.95/3.60 7.95/3.60 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 /\\ ar_0 - ar_1 >= 0 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-2) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-2) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-2) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-3) = 1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-2) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-3) = 1 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-2) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ar_1 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ar_0 7.95/3.60 7.95/3.60 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-3) = ar_3 7.95/3.60 7.95/3.60 orients the transitions 7.95/3.60 7.95/3.60 evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 7.95/3.60 7.95/3.60 weakly and the transition 7.95/3.60 7.95/3.60 evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 7.95/3.60 7.95/3.60 strictly and produces the following problem: 7.95/3.60 7.95/3.60 35: T: 7.95/3.60 7.95/3.60 (Comp: 2, Cost: 2) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 7.95/3.60 7.95/3.60 (Comp: 2*ar_0 + 1, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 7.95/3.60 7.95/3.60 (Comp: 2*ar_1 + 2*ar_0 + 2*ar_0*ar_1 + 2*ar_0^2, Cost: 2) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 3) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 7.95/3.60 7.95/3.60 (Comp: 2*ar_0 + 1, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 7.95/3.60 7.95/3.60 (Comp: 2*ar_0 + 1, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 /\ ar_0 - ar_1 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 2) evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 4) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 /\ -ar_0 >= 0 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 7.95/3.60 7.95/3.60 (Comp: 1, Cost: 5) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 7.95/3.60 7.95/3.60 start location: koat_start 7.95/3.60 7.95/3.60 leaf cost: 0 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Complexity upper bound 10*ar_0 + 4*ar_1 + 4*ar_0*ar_1 + 4*ar_0^2 + 26 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Time: 1.526 sec (SMT: 1.111 sec) 7.95/3.60 7.95/3.60 7.95/3.60 ---------------------------------------- 7.95/3.60 7.95/3.60 (2) 7.95/3.60 BOUNDS(1, n^2) 7.95/3.60 7.95/3.60 ---------------------------------------- 7.95/3.60 7.95/3.60 (3) Loat Proof (FINISHED) 7.95/3.60 7.95/3.60 7.95/3.60 ### Pre-processing the ITS problem ### 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Initial linear ITS problem 7.95/3.60 7.95/3.60 Start location: evalstartstart 7.95/3.60 7.95/3.60 0: evalstartstart -> evalstartbb0in : [], cost: 1 7.95/3.60 7.95/3.60 1: evalstartbb0in -> evalstart0 : [], cost: 1 7.95/3.60 7.95/3.60 2: evalstart0 -> evalstart1 : [], cost: 1 7.95/3.60 7.95/3.60 3: evalstart1 -> evalstart2 : [], cost: 1 7.95/3.60 7.95/3.60 4: evalstart2 -> evalstart3 : [], cost: 1 7.95/3.60 7.95/3.60 5: evalstart3 -> evalstartbb1in : [ A>=1 ], cost: 1 7.95/3.60 7.95/3.60 6: evalstart3 -> evalstartbb6in : [ 0>=A ], cost: 1 7.95/3.60 7.95/3.60 7: evalstartbb1in -> evalstartbb2in : C'=A, [ B>=1+A ], cost: 1 7.95/3.60 7.95/3.60 8: evalstartbb1in -> evalstartbb5in : [ A>=B ], cost: 1 7.95/3.60 7.95/3.60 9: evalstartbb2in -> evalstartbb3in : [ C>=1 && B>=1+C ], cost: 1 7.95/3.60 7.95/3.60 10: evalstartbb2in -> evalstartbb4in : [ 0>=C ], cost: 1 7.95/3.60 7.95/3.60 11: evalstartbb2in -> evalstartbb4in : [ C>=B ], cost: 1 7.95/3.60 7.95/3.60 12: evalstartbb3in -> evalstartbb2in : C'=1+C, [ D==1 ], cost: 1 7.95/3.60 7.95/3.60 13: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ 0>=D ], cost: 1 7.95/3.60 7.95/3.60 14: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ D>=2 ], cost: 1 7.95/3.60 7.95/3.60 15: evalstartbb4in -> evalstartstop : [], cost: 1 7.95/3.60 7.95/3.60 16: evalstartbb5in -> evalstart8 : [], cost: 1 7.95/3.60 7.95/3.60 17: evalstart8 -> evalstart9 : [], cost: 1 7.95/3.60 7.95/3.60 18: evalstart9 -> evalstartstop : [], cost: 1 7.95/3.60 7.95/3.60 19: evalstartbb6in -> evalstart10 : [], cost: 1 7.95/3.60 7.95/3.60 20: evalstart10 -> evalstart11 : [], cost: 1 7.95/3.60 7.95/3.60 21: evalstart11 -> evalstartstop : [], cost: 1 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Removed unreachable and leaf rules: 7.95/3.60 7.95/3.60 Start location: evalstartstart 7.95/3.60 7.95/3.60 0: evalstartstart -> evalstartbb0in : [], cost: 1 7.95/3.60 7.95/3.60 1: evalstartbb0in -> evalstart0 : [], cost: 1 7.95/3.60 7.95/3.60 2: evalstart0 -> evalstart1 : [], cost: 1 7.95/3.60 7.95/3.60 3: evalstart1 -> evalstart2 : [], cost: 1 7.95/3.60 7.95/3.60 4: evalstart2 -> evalstart3 : [], cost: 1 7.95/3.60 7.95/3.60 5: evalstart3 -> evalstartbb1in : [ A>=1 ], cost: 1 7.95/3.60 7.95/3.60 7: evalstartbb1in -> evalstartbb2in : C'=A, [ B>=1+A ], cost: 1 7.95/3.60 7.95/3.60 9: evalstartbb2in -> evalstartbb3in : [ C>=1 && B>=1+C ], cost: 1 7.95/3.60 7.95/3.60 12: evalstartbb3in -> evalstartbb2in : C'=1+C, [ D==1 ], cost: 1 7.95/3.60 7.95/3.60 13: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ 0>=D ], cost: 1 7.95/3.60 7.95/3.60 14: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ D>=2 ], cost: 1 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 ### Simplification by acceleration and chaining ### 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Eliminated locations (on linear paths): 7.95/3.60 7.95/3.60 Start location: evalstartstart 7.95/3.60 7.95/3.60 27: evalstartstart -> evalstartbb2in : C'=A, [ A>=1 && B>=1+A ], cost: 7 7.95/3.60 7.95/3.60 9: evalstartbb2in -> evalstartbb3in : [ C>=1 && B>=1+C ], cost: 1 7.95/3.60 7.95/3.60 12: evalstartbb3in -> evalstartbb2in : C'=1+C, [ D==1 ], cost: 1 7.95/3.60 7.95/3.60 13: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ 0>=D ], cost: 1 7.95/3.60 7.95/3.60 14: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ D>=2 ], cost: 1 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Eliminated locations (on tree-shaped paths): 7.95/3.60 7.95/3.60 Start location: evalstartstart 7.95/3.60 7.95/3.60 27: evalstartstart -> evalstartbb2in : C'=A, [ A>=1 && B>=1+A ], cost: 7 7.95/3.60 7.95/3.60 28: evalstartbb2in -> evalstartbb2in : C'=1+C, [ C>=1 && B>=1+C && D==1 ], cost: 2 7.95/3.60 7.95/3.60 29: evalstartbb2in -> evalstartbb2in : C'=-1+C, [ C>=1 && B>=1+C && 0>=D ], cost: 2 7.95/3.60 7.95/3.60 30: evalstartbb2in -> evalstartbb2in : C'=-1+C, [ C>=1 && B>=1+C && D>=2 ], cost: 2 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Accelerating simple loops of location 7. 7.95/3.60 7.95/3.60 Accelerating the following rules: 7.95/3.60 7.95/3.60 28: evalstartbb2in -> evalstartbb2in : C'=1+C, [ C>=1 && B>=1+C && D==1 ], cost: 2 7.95/3.60 7.95/3.60 29: evalstartbb2in -> evalstartbb2in : C'=-1+C, [ C>=1 && B>=1+C && 0>=D ], cost: 2 7.95/3.60 7.95/3.60 30: evalstartbb2in -> evalstartbb2in : C'=-1+C, [ C>=1 && B>=1+C && D>=2 ], cost: 2 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Accelerated rule 28 with metering function -C+B, yielding the new rule 31. 7.95/3.60 7.95/3.60 Accelerated rule 29 with metering function C, yielding the new rule 32. 7.95/3.60 7.95/3.60 Accelerated rule 30 with metering function C, yielding the new rule 33. 7.95/3.60 7.95/3.60 Removing the simple loops: 28 29 30. 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Accelerated all simple loops using metering functions (where possible): 7.95/3.60 7.95/3.60 Start location: evalstartstart 7.95/3.60 7.95/3.60 27: evalstartstart -> evalstartbb2in : C'=A, [ A>=1 && B>=1+A ], cost: 7 7.95/3.60 7.95/3.60 31: evalstartbb2in -> evalstartbb2in : C'=B, [ C>=1 && B>=1+C && D==1 ], cost: -2*C+2*B 7.95/3.60 7.95/3.60 32: evalstartbb2in -> evalstartbb2in : C'=0, [ C>=1 && B>=1+C && 0>=D ], cost: 2*C 7.95/3.60 7.95/3.60 33: evalstartbb2in -> evalstartbb2in : C'=0, [ C>=1 && B>=1+C && D>=2 ], cost: 2*C 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Chained accelerated rules (with incoming rules): 7.95/3.60 7.95/3.60 Start location: evalstartstart 7.95/3.60 7.95/3.60 27: evalstartstart -> evalstartbb2in : C'=A, [ A>=1 && B>=1+A ], cost: 7 7.95/3.60 7.95/3.60 34: evalstartstart -> evalstartbb2in : C'=B, [ A>=1 && B>=1+A && D==1 ], cost: 7-2*A+2*B 7.95/3.60 7.95/3.60 35: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && 0>=D ], cost: 7+2*A 7.95/3.60 7.95/3.60 36: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && D>=2 ], cost: 7+2*A 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Removed unreachable locations (and leaf rules with constant cost): 7.95/3.60 7.95/3.60 Start location: evalstartstart 7.95/3.60 7.95/3.60 34: evalstartstart -> evalstartbb2in : C'=B, [ A>=1 && B>=1+A && D==1 ], cost: 7-2*A+2*B 7.95/3.60 7.95/3.60 35: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && 0>=D ], cost: 7+2*A 7.95/3.60 7.95/3.60 36: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && D>=2 ], cost: 7+2*A 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 ### Computing asymptotic complexity ### 7.95/3.60 7.95/3.60 7.95/3.60 7.95/3.60 Fully simplified ITS problem 7.95/3.60 7.95/3.60 Start location: evalstartstart 7.95/3.60 7.95/3.60 34: evalstartstart -> evalstartbb2in : C'=B, [ A>=1 && B>=1+A && D==1 ], cost: 7-2*A+2*B 7.95/3.60 7.95/3.60 35: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && 0>=D ], cost: 7+2*A 7.95/3.60 7.95/3.60 36: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && D>=2 ], cost: 7+2*A 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 Computing asymptotic complexity for rule 34 8.07/3.60 8.07/3.60 Solved the limit problem by the following transformations: 8.07/3.60 8.07/3.60 Created initial limit problem: 8.07/3.60 8.07/3.60 2-D (+/+!), D (+/+!), 7-2*A+2*B (+), A (+/+!), -A+B (+/+!) [not solved] 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 applying transformation rule (C) using substitution {D==1} 8.07/3.60 8.07/3.60 resulting limit problem: 8.07/3.60 8.07/3.60 1 (+/+!), 7-2*A+2*B (+), A (+/+!), -A+B (+/+!) [not solved] 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 applying transformation rule (C) using substitution {A==1} 8.07/3.60 8.07/3.60 resulting limit problem: 8.07/3.60 8.07/3.60 1 (+/+!), 5+2*B (+), -1+B (+/+!) [not solved] 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 applying transformation rule (C) using substitution {B==1+A} 8.07/3.60 8.07/3.60 resulting limit problem: 8.07/3.60 8.07/3.60 1 (+/+!), 7+2*A (+), A (+/+!) [not solved] 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 applying transformation rule (B), deleting 1 (+/+!) 8.07/3.60 8.07/3.60 resulting limit problem: 8.07/3.60 8.07/3.60 7+2*A (+), A (+/+!) [not solved] 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 applying transformation rule (D), replacing 7+2*A (+) by 2*A (+) 8.07/3.60 8.07/3.60 resulting limit problem: 8.07/3.60 8.07/3.60 2*A (+), A (+/+!) [not solved] 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 applying transformation rule (A), replacing 2*A (+) by A (+) and 2 (+!) using + limit vector (+,+!) 8.07/3.60 8.07/3.60 resulting limit problem: 8.07/3.60 8.07/3.60 2 (+!), A (+) [not solved] 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 applying transformation rule (B), deleting 2 (+!) 8.07/3.60 8.07/3.60 resulting limit problem: 8.07/3.60 8.07/3.60 A (+) [solved] 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 Solution: 8.07/3.60 8.07/3.60 D / 1 8.07/3.60 8.07/3.60 A / 1 8.07/3.60 8.07/3.60 B / 1+n 8.07/3.60 8.07/3.60 Resulting cost 7+2*n has complexity: Poly(n^1) 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 Found new complexity Poly(n^1). 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 Obtained the following overall complexity (w.r.t. the length of the input n): 8.07/3.60 8.07/3.60 Complexity: Poly(n^1) 8.07/3.60 8.07/3.60 Cpx degree: 1 8.07/3.60 8.07/3.60 Solved cost: 7+2*n 8.07/3.60 8.07/3.60 Rule cost: 7-2*A+2*B 8.07/3.60 8.07/3.60 Rule guard: [ A>=1 && B>=1+A && D==1 ] 8.07/3.60 8.07/3.60 8.07/3.60 8.07/3.60 WORST_CASE(Omega(n^1),?) 8.07/3.60 8.07/3.60 8.07/3.60 ---------------------------------------- 8.07/3.60 8.07/3.60 (4) 8.07/3.60 BOUNDS(n^1, INF) 8.07/3.65 EOF