2.15/1.30 WORST_CASE(?, O(n^2)) 2.15/1.31 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.15/1.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.15/1.31 2.15/1.31 2.15/1.31 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.15/1.31 2.15/1.31 (0) CpxIntTrs 2.15/1.31 (1) Koat Proof [FINISHED, 75 ms] 2.15/1.31 (2) BOUNDS(1, n^2) 2.15/1.31 2.15/1.31 2.15/1.31 ---------------------------------------- 2.15/1.31 2.15/1.31 (0) 2.15/1.31 Obligation: 2.15/1.31 Complexity Int TRS consisting of the following rules: 2.15/1.31 eval_foo_start(v_.0, v_K, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_K, v_x)) :|: TRUE 2.15/1.31 eval_foo_bb0_in(v_.0, v_K, v_x) -> Com_1(eval_foo_bb1_in(v_x, v_K, v_x)) :|: TRUE 2.15/1.31 eval_foo_bb1_in(v_.0, v_K, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_K, v_x)) :|: v_.0 < v_K 2.15/1.31 eval_foo_bb1_in(v_.0, v_K, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_K, v_x)) :|: v_.0 > v_K 2.15/1.31 eval_foo_bb1_in(v_.0, v_K, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_K, v_x)) :|: v_.0 >= v_K && v_.0 <= v_K 2.15/1.31 eval_foo_bb2_in(v_.0, v_K, v_x) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_K, v_x)) :|: v_.0 > v_K 2.15/1.31 eval_foo_bb2_in(v_.0, v_K, v_x) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_K, v_x)) :|: v_.0 <= v_K 2.15/1.31 eval_foo_bb3_in(v_.0, v_K, v_x) -> Com_1(eval_foo_stop(v_.0, v_K, v_x)) :|: TRUE 2.15/1.31 2.15/1.31 The start-symbols are:[eval_foo_start_3] 2.15/1.31 2.15/1.31 2.15/1.31 ---------------------------------------- 2.15/1.31 2.15/1.31 (1) Koat Proof (FINISHED) 2.15/1.31 YES(?, 176*ar_1 + 184*ar_2 + 24*ar_1^2 + 56*ar_1*ar_2 + 32*ar_2^2 + 154) 2.15/1.31 2.15/1.31 2.15/1.31 2.15/1.31 Initial complexity problem: 2.15/1.31 2.15/1.31 1: T: 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.15/1.31 2.15/1.31 start location: koat_start 2.15/1.31 2.15/1.31 leaf cost: 0 2.15/1.31 2.15/1.31 2.15/1.31 2.15/1.31 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.15/1.31 2.15/1.31 2: T: 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.15/1.31 2.15/1.31 start location: koat_start 2.15/1.31 2.15/1.31 leaf cost: 0 2.15/1.31 2.15/1.31 2.15/1.31 2.15/1.31 A polynomial rank function with 2.15/1.31 2.15/1.31 Pol(evalfoostart) = 2 2.15/1.31 2.15/1.31 Pol(evalfoobb0in) = 2 2.15/1.31 2.15/1.31 Pol(evalfoobb1in) = 2 2.15/1.31 2.15/1.31 Pol(evalfoobb2in) = 2 2.15/1.31 2.15/1.31 Pol(evalfoobb3in) = 1 2.15/1.31 2.15/1.31 Pol(evalfoostop) = 0 2.15/1.31 2.15/1.31 Pol(koat_start) = 2 2.15/1.31 2.15/1.31 orients all transitions weakly and the transitions 2.15/1.31 2.15/1.31 evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ] 2.15/1.31 2.15/1.31 strictly and produces the following problem: 2.15/1.31 2.15/1.31 3: T: 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.15/1.31 2.15/1.31 (Comp: 2, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.15/1.31 2.15/1.31 start location: koat_start 2.15/1.31 2.15/1.31 leaf cost: 0 2.15/1.31 2.15/1.31 2.15/1.31 2.15/1.31 A polynomial rank function with 2.15/1.31 2.15/1.31 Pol(evalfoobb1in) = -2*V_1 + 2*V_3 + 2 2.15/1.31 2.15/1.31 Pol(evalfoobb2in) = -2*V_1 + 2*V_3 + 1 2.15/1.31 2.15/1.31 and size complexities 2.15/1.31 2.15/1.31 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0 2.15/1.31 2.15/1.31 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ? 2.15/1.31 2.15/1.31 S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ]", 0-0) = ? 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ? 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ]", 0-0) = ? 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ? 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-0) = ? 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0 2.15/1.31 2.15/1.31 S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2 2.15/1.31 2.15/1.31 orients the transitions 2.15/1.31 2.15/1.31 evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] 2.15/1.31 2.15/1.31 evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.15/1.31 2.15/1.31 weakly and the transitions 2.15/1.31 2.15/1.31 evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.15/1.31 2.15/1.31 evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] 2.15/1.31 2.15/1.31 strictly and produces the following problem: 2.15/1.31 2.15/1.31 4: T: 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 2*ar_1 + 2*ar_2 + 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ] 2.15/1.31 2.15/1.31 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 (Comp: 2*ar_1 + 2*ar_2 + 2, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.15/1.31 2.15/1.31 (Comp: 2, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.15/1.31 2.15/1.31 start location: koat_start 2.15/1.31 2.15/1.31 leaf cost: 0 2.15/1.31 2.15/1.31 2.15/1.31 2.15/1.31 A polynomial rank function with 2.15/1.31 2.15/1.31 Pol(evalfoobb2in) = 2*V_1 - 2*V_3 - 1 2.15/1.31 2.15/1.31 Pol(evalfoobb1in) = 2*V_1 - 2*V_3 2.15/1.31 2.15/1.31 and size complexities 2.15/1.31 2.15/1.31 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0 2.15/1.31 2.15/1.31 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ? 2.15/1.31 2.15/1.31 S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ]", 0-0) = 3*ar_1 + 3*ar_2 + 18 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ? 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ]", 0-0) = ? 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ? 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-0) = 3*ar_1 + 3*ar_2 + 18 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2 2.15/1.31 2.15/1.31 S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0 2.15/1.31 2.15/1.31 S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1 2.15/1.31 2.15/1.31 S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2 2.15/1.31 2.15/1.31 orients the transitions 2.15/1.31 2.15/1.31 evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 weakly and the transitions 2.15/1.31 2.15/1.31 evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 strictly and produces the following problem: 2.15/1.31 2.15/1.31 5: T: 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 2*ar_1 + 2*ar_2 + 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] 2.15/1.31 2.15/1.31 (Comp: 12*ar_1^2 + 28*ar_1*ar_2 + 16*ar_2^2 + 86*ar_1 + 90*ar_2 + 72, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = ar_2 ] 2.15/1.31 2.15/1.31 (Comp: 12*ar_1^2 + 28*ar_1*ar_2 + 16*ar_2^2 + 86*ar_1 + 90*ar_2 + 72, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.15/1.31 2.15/1.31 (Comp: 2*ar_1 + 2*ar_2 + 2, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.15/1.31 2.15/1.31 (Comp: 2, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.15/1.31 2.15/1.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.15/1.31 2.15/1.31 start location: koat_start 2.15/1.31 2.15/1.31 leaf cost: 0 2.15/1.31 2.15/1.31 2.15/1.31 2.15/1.31 Complexity upper bound 176*ar_1 + 184*ar_2 + 24*ar_1^2 + 56*ar_1*ar_2 + 32*ar_2^2 + 154 2.15/1.31 2.15/1.31 2.15/1.31 2.15/1.31 Time: 0.091 sec (SMT: 0.082 sec) 2.15/1.31 2.15/1.31 2.15/1.31 ---------------------------------------- 2.15/1.31 2.15/1.31 (2) 2.15/1.31 BOUNDS(1, n^2) 2.15/1.33 EOF