2.13/1.38 WORST_CASE(?, O(n^2)) 2.28/1.39 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.28/1.39 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.28/1.39 2.28/1.39 2.28/1.39 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.28/1.39 2.28/1.39 (0) CpxIntTrs 2.28/1.39 (1) Koat Proof [FINISHED, 84 ms] 2.28/1.39 (2) BOUNDS(1, n^2) 2.28/1.39 2.28/1.39 2.28/1.39 ---------------------------------------- 2.28/1.39 2.28/1.39 (0) 2.28/1.39 Obligation: 2.28/1.39 Complexity Int TRS consisting of the following rules: 2.28/1.39 eval_foo_start(v_.0, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_x)) :|: TRUE 2.28/1.39 eval_foo_bb0_in(v_.0, v_x) -> Com_1(eval_foo_bb1_in(v_x, v_x)) :|: TRUE 2.28/1.39 eval_foo_bb1_in(v_.0, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_x)) :|: v_.0 < 0 2.28/1.39 eval_foo_bb1_in(v_.0, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_x)) :|: v_.0 > 0 2.28/1.39 eval_foo_bb1_in(v_.0, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_x)) :|: v_.0 >= 0 && v_.0 <= 0 2.28/1.39 eval_foo_bb2_in(v_.0, v_x) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_x)) :|: v_.0 > 0 2.28/1.39 eval_foo_bb2_in(v_.0, v_x) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_x)) :|: v_.0 <= 0 2.28/1.39 eval_foo_bb3_in(v_.0, v_x) -> Com_1(eval_foo_stop(v_.0, v_x)) :|: TRUE 2.28/1.39 2.28/1.39 The start-symbols are:[eval_foo_start_2] 2.28/1.39 2.28/1.39 2.28/1.39 ---------------------------------------- 2.28/1.39 2.28/1.39 (1) Koat Proof (FINISHED) 2.28/1.39 YES(?, 28*ar_1 + 8*ar_1^2 + 24) 2.28/1.39 2.28/1.39 2.28/1.39 2.28/1.39 Initial complexity problem: 2.28/1.39 2.28/1.39 1: T: 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1)) 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ ar_0 = 0 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ] 2.28/1.39 2.28/1.39 start location: koat_start 2.28/1.39 2.28/1.39 leaf cost: 0 2.28/1.39 2.28/1.39 2.28/1.39 2.28/1.39 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.28/1.39 2.28/1.39 2: T: 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1)) 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ ar_0 = 0 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ] 2.28/1.39 2.28/1.39 start location: koat_start 2.28/1.39 2.28/1.39 leaf cost: 0 2.28/1.39 2.28/1.39 2.28/1.39 2.28/1.39 A polynomial rank function with 2.28/1.39 2.28/1.39 Pol(evalfoostart) = 2 2.28/1.39 2.28/1.39 Pol(evalfoobb0in) = 2 2.28/1.39 2.28/1.39 Pol(evalfoobb1in) = 2 2.28/1.39 2.28/1.39 Pol(evalfoobb2in) = 2 2.28/1.39 2.28/1.39 Pol(evalfoobb3in) = 1 2.28/1.39 2.28/1.39 Pol(evalfoostop) = 0 2.28/1.39 2.28/1.39 Pol(koat_start) = 2 2.28/1.39 2.28/1.39 orients all transitions weakly and the transitions 2.28/1.39 2.28/1.39 evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) 2.28/1.39 2.28/1.39 evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ ar_0 = 0 ] 2.28/1.39 2.28/1.39 strictly and produces the following problem: 2.28/1.39 2.28/1.39 3: T: 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1)) 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ ar_0 = 0 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ] 2.28/1.39 2.28/1.39 (Comp: 2, Cost: 1) evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ] 2.28/1.39 2.28/1.39 start location: koat_start 2.28/1.39 2.28/1.39 leaf cost: 0 2.28/1.39 2.28/1.39 2.28/1.39 2.28/1.39 A polynomial rank function with 2.28/1.39 2.28/1.39 Pol(evalfoobb1in) = -2*V_1 + 2 2.28/1.39 2.28/1.39 Pol(evalfoobb2in) = -2*V_1 + 1 2.28/1.39 2.28/1.39 and size complexities 2.28/1.39 2.28/1.39 S("koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]", 0-0) = ar_0 2.28/1.39 2.28/1.39 S("koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))", 0-0) = 0 2.28/1.39 2.28/1.39 S("evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ]", 0-0) = ar_1 + 1 2.28/1.39 2.28/1.39 S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ]", 0-0) = ar_1 + 1 2.28/1.39 2.28/1.39 S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ ar_0 = 0 ]", 0-0) = 0 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ ar_0 = 0 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ]", 0-0) = ar_1 + 1 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_1 + 1 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))", 0-0) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))", 0-0) = ar_0 2.28/1.39 2.28/1.39 S("evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))", 0-1) = ar_1 2.28/1.39 2.28/1.39 orients the transitions 2.28/1.39 2.28/1.39 evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ] 2.28/1.39 2.28/1.39 evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ] 2.28/1.39 2.28/1.39 weakly and the transitions 2.28/1.39 2.28/1.39 evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ] 2.28/1.39 2.28/1.39 evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ] 2.28/1.39 2.28/1.39 strictly and produces the following problem: 2.28/1.39 2.28/1.39 4: T: 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ ar_0 = 0 ] 2.28/1.39 2.28/1.39 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ] 2.28/1.39 2.28/1.39 (Comp: 2, Cost: 1) evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ] 2.28/1.39 2.28/1.39 start location: koat_start 2.28/1.39 2.28/1.39 leaf cost: 0 2.28/1.39 2.28/1.39 2.28/1.39 2.28/1.39 A polynomial rank function with 2.28/1.39 2.28/1.39 Pol(evalfoobb2in) = 2*V_1 2.28/1.39 2.28/1.39 Pol(evalfoobb1in) = 2*V_1 + 1 2.28/1.39 2.28/1.39 and size complexities 2.28/1.39 2.28/1.39 S("koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]", 0-0) = ar_0 2.28/1.39 2.28/1.39 S("koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))", 0-0) = 0 2.28/1.39 2.28/1.39 S("evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ]", 0-0) = ar_1 + 1 2.28/1.39 2.28/1.39 S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ]", 0-0) = ar_1 + 1 2.28/1.39 2.28/1.39 S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ ar_0 = 0 ]", 0-0) = 0 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ ar_0 = 0 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ]", 0-0) = ar_1 + 1 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_1 + 1 2.28/1.39 2.28/1.39 S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))", 0-0) = ar_1 2.28/1.39 2.28/1.39 S("evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1))", 0-1) = ar_1 2.28/1.39 2.28/1.39 S("evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))", 0-0) = ar_0 2.28/1.39 2.28/1.39 S("evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))", 0-1) = ar_1 2.28/1.39 2.28/1.39 orients the transitions 2.28/1.39 2.28/1.39 evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 weakly and the transitions 2.28/1.39 2.28/1.39 evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 strictly and produces the following problem: 2.28/1.39 2.28/1.39 5: T: 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_1, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ 0 >= ar_0 + 1 ] 2.28/1.39 2.28/1.39 (Comp: 4*ar_1^2 + 12*ar_1 + 7, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ ar_0 = 0 ] 2.28/1.39 2.28/1.39 (Comp: 4*ar_1^2 + 12*ar_1 + 7, Cost: 1) evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1)) [ ar_0 >= 1 ] 2.28/1.39 2.28/1.39 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1)) [ 0 >= ar_0 ] 2.28/1.39 2.28/1.39 (Comp: 2, Cost: 1) evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1)) 2.28/1.39 2.28/1.39 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ] 2.28/1.39 2.28/1.39 start location: koat_start 2.28/1.39 2.28/1.39 leaf cost: 0 2.28/1.39 2.28/1.39 2.28/1.39 2.28/1.39 Complexity upper bound 28*ar_1 + 8*ar_1^2 + 24 2.28/1.39 2.28/1.39 2.28/1.39 2.28/1.39 Time: 0.106 sec (SMT: 0.099 sec) 2.28/1.39 2.28/1.39 2.28/1.39 ---------------------------------------- 2.28/1.39 2.28/1.39 (2) 2.28/1.39 BOUNDS(1, n^2) 2.28/1.41 EOF