/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 176 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_c, v_x)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_x, 1, v_c, v_x)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_c, v_x)) :|: v_.01 > 0 eval_foo_bb1_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_c, v_x)) :|: v_.01 <= 0 eval_foo_bb2_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_c, v_x)) :|: v_.0 > 100 eval_foo_bb2_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_c, v_x)) :|: v_.0 <= 100 eval_foo_bb3_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_.0 - 10, v_.01 - 1, v_c, v_x)) :|: TRUE eval_foo_bb4_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_.0 + 11, v_.01 + 1, v_c, v_x)) :|: TRUE eval_foo_bb5_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_stop(v_.0, v_.01, v_c, v_x)) :|: TRUE The start-symbols are:[eval_foo_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 18256*ar_1 + 36*ar_1^2 + 1476635) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 2 Pol(evalfoobb0in) = 2 Pol(evalfoobb1in) = 2 Pol(evalfoobb2in) = 2 Pol(evalfoobb5in) = 1 Pol(evalfoobb3in) = 2 Pol(evalfoobb4in) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) (Comp: 2, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalfoobb2in: X_3 - 1 >= 0 For symbol evalfoobb3in: X_3 - 1 >= 0 /\ X_1 + X_3 - 102 >= 0 /\ X_1 - 101 >= 0 For symbol evalfoobb4in: X_3 - 1 >= 0 /\ -X_1 + X_3 + 99 >= 0 /\ -X_1 + 100 >= 0 For symbol evalfoobb5in: -X_3 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 99 >= 0 /\ -ar_0 + 100 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - 101 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ 100 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_0 >= 101 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -2*V_2 + 202 Pol(evalfoostart) = -2*V_2 + 202 Pol(evalfoobb5in) = -2*V_1 + 20*V_3 Pol(evalfoostop) = -2*V_1 + 20*V_3 Pol(evalfoobb4in) = -2*V_1 + 20*V_3 + 181 Pol(evalfoobb1in) = -2*V_1 + 20*V_3 + 182 Pol(evalfoobb3in) = -2*V_1 + 20*V_3 + 182 Pol(evalfoobb2in) = -2*V_1 + 20*V_3 + 182 Pol(evalfoobb0in) = -2*V_2 + 202 orients all transitions weakly and the transitions evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 99 >= 0 /\ -ar_0 + 100 >= 0 ] evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ 100 >= ar_0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ] (Comp: 2*ar_1 + 202, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 99 >= 0 /\ -ar_0 + 100 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - 101 >= 0 ] (Comp: 2*ar_1 + 202, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ 100 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_0 >= 101 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb3in) = 3*V_3 - 2 Pol(evalfoobb1in) = 3*V_3 Pol(evalfoobb2in) = 3*V_3 - 1 and size complexities S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0 S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1 S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2 S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))", 0-0) = ar_1 S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))", 0-1) = ar_1 S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))", 0-2) = 1 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]", 0-0) = ar_1 + 111 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]", 0-1) = ar_1 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]", 0-2) = 2*ar_1 + 812 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-0) = ar_1 + 111 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-1) = ar_1 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-2) = 2*ar_1 + 1624 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_0 >= 101 ]", 0-0) = ar_1 + 111 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_0 >= 101 ]", 0-1) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_0 >= 101 ]", 0-2) = 2*ar_1 + 812 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ 100 >= ar_0 ]", 0-0) = ar_1 + 111 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ 100 >= ar_0 ]", 0-1) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ 100 >= ar_0 ]", 0-2) = 2*ar_1 + 812 S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 102 >= 0 /\\ ar_0 - 101 >= 0 ]", 0-0) = ar_1 + 111 S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 102 >= 0 /\\ ar_0 - 101 >= 0 ]", 0-1) = ar_1 S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 102 >= 0 /\\ ar_0 - 101 >= 0 ]", 0-2) = 2*ar_1 + 812 S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 99 >= 0 /\\ -ar_0 + 100 >= 0 ]", 0-0) = ar_1 + 111 S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 99 >= 0 /\\ -ar_0 + 100 >= 0 ]", 0-1) = ar_1 S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 99 >= 0 /\\ -ar_0 + 100 >= 0 ]", 0-2) = 2*ar_1 + 812 S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ]", 0-0) = ar_1 + 111 S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ]", 0-1) = ar_1 S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ]", 0-2) = 2*ar_1 + 3248 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2 orients the transitions evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - 101 >= 0 ] evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_0 >= 101 ] evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] weakly and the transitions evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - 101 >= 0 ] evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_0 >= 101 ] evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ] (Comp: 2*ar_1 + 202, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 99 >= 0 /\ -ar_0 + 100 >= 0 ] (Comp: 12*ar_1^2 + 6084*ar_1 + 492075, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - 101 >= 0 ] (Comp: 2*ar_1 + 202, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ 100 >= ar_0 ] (Comp: 12*ar_1^2 + 6084*ar_1 + 492075, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_0 >= 101 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] (Comp: 12*ar_1^2 + 6084*ar_1 + 492075, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) start location: koat_start leaf cost: 0 Complexity upper bound 18256*ar_1 + 36*ar_1^2 + 1476635 Time: 0.217 sec (SMT: 0.196 sec) ---------------------------------------- (2) BOUNDS(1, n^2)