2.45/1.44 WORST_CASE(?, O(n^2)) 2.45/1.45 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.45/1.45 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.45/1.45 2.45/1.45 2.45/1.45 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.45/1.45 2.45/1.45 (0) CpxIntTrs 2.45/1.45 (1) Koat Proof [FINISHED, 179 ms] 2.45/1.45 (2) BOUNDS(1, n^2) 2.45/1.45 2.45/1.45 2.45/1.45 ---------------------------------------- 2.45/1.45 2.45/1.45 (0) 2.45/1.45 Obligation: 2.45/1.45 Complexity Int TRS consisting of the following rules: 2.45/1.45 eval_foo_start(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.1, v_x, v_y)) :|: TRUE 2.45/1.45 eval_foo_bb0_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.1, v_x, v_y)) :|: TRUE 2.45/1.45 eval_foo_bb1_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, 1, v_x, v_y)) :|: v_.0 >= 0 && v_.01 > 0 2.45/1.45 eval_foo_bb1_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.1, v_x, v_y)) :|: v_.0 < 0 2.45/1.45 eval_foo_bb1_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.1, v_x, v_y)) :|: v_.01 <= 0 2.45/1.45 eval_foo_bb2_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.1, v_x, v_y)) :|: v_.0 > v_.1 && v_.1 > 0 2.45/1.45 eval_foo_bb2_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.1, v_x, v_y)) :|: v_.0 <= v_.1 2.45/1.45 eval_foo_bb2_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.1, v_x, v_y)) :|: v_.1 <= 0 2.45/1.45 eval_foo_bb3_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, 2 * v_.1, v_x, v_y)) :|: TRUE 2.45/1.45 eval_foo_bb4_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.1, v_.1, v_x, v_y)) :|: TRUE 2.45/1.45 eval_foo_bb5_in(v_.0, v_.01, v_.1, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.1, v_x, v_y)) :|: TRUE 2.45/1.45 2.45/1.45 The start-symbols are:[eval_foo_start_5] 2.45/1.45 2.45/1.45 2.45/1.45 ---------------------------------------- 2.45/1.45 2.45/1.45 (1) Koat Proof (FINISHED) 2.45/1.45 YES(?, 51*ar_1 + 6*ar_1^2 + 53) 2.45/1.45 2.45/1.45 2.45/1.45 2.45/1.45 Initial complexity problem: 2.45/1.45 2.45/1.45 1: T: 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\ ar_2 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\ ar_4 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4)) 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.45/1.45 2.45/1.45 start location: koat_start 2.45/1.45 2.45/1.45 leaf cost: 0 2.45/1.45 2.45/1.45 2.45/1.45 2.45/1.45 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.45/1.45 2.45/1.45 2: T: 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\ ar_2 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\ ar_4 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4)) 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.45/1.45 2.45/1.45 start location: koat_start 2.45/1.45 2.45/1.45 leaf cost: 0 2.45/1.45 2.45/1.45 2.45/1.45 2.45/1.45 A polynomial rank function with 2.45/1.45 2.45/1.45 Pol(evalfoostart) = 2 2.45/1.45 2.45/1.45 Pol(evalfoobb0in) = 2 2.45/1.45 2.45/1.45 Pol(evalfoobb1in) = 2 2.45/1.45 2.45/1.45 Pol(evalfoobb2in) = 2 2.45/1.45 2.45/1.45 Pol(evalfoobb5in) = 1 2.45/1.45 2.45/1.45 Pol(evalfoobb3in) = 2 2.45/1.45 2.45/1.45 Pol(evalfoobb4in) = 2 2.45/1.45 2.45/1.45 Pol(evalfoostop) = 0 2.45/1.45 2.45/1.45 Pol(koat_start) = 2 2.45/1.45 2.45/1.45 orients all transitions weakly and the transitions 2.45/1.45 2.45/1.45 evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.45/1.45 2.45/1.45 evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] 2.45/1.45 2.45/1.45 strictly and produces the following problem: 2.45/1.45 2.45/1.45 3: T: 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\ ar_2 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\ ar_4 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4)) 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.45/1.45 2.45/1.45 start location: koat_start 2.45/1.45 2.45/1.45 leaf cost: 0 2.45/1.45 2.45/1.45 2.45/1.45 2.45/1.45 A polynomial rank function with 2.45/1.45 2.45/1.45 Pol(evalfoostart) = V_2 + 1 2.45/1.45 2.45/1.45 Pol(evalfoobb0in) = V_2 + 1 2.45/1.45 2.45/1.45 Pol(evalfoobb1in) = V_1 + 1 2.45/1.45 2.45/1.45 Pol(evalfoobb2in) = V_1 2.45/1.45 2.45/1.45 Pol(evalfoobb5in) = V_1 2.45/1.45 2.45/1.45 Pol(evalfoobb3in) = V_1 2.45/1.45 2.45/1.45 Pol(evalfoobb4in) = V_1 2.45/1.45 2.45/1.45 Pol(evalfoostop) = V_1 2.45/1.45 2.45/1.45 Pol(koat_start) = V_2 + 1 2.45/1.45 2.45/1.45 orients all transitions weakly and the transition 2.45/1.45 2.45/1.45 evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\ ar_2 >= 1 ] 2.45/1.45 2.45/1.45 strictly and produces the following problem: 2.45/1.45 2.45/1.45 4: T: 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: ar_1 + 1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\ ar_2 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\ ar_4 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4)) 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.45/1.45 2.45/1.45 start location: koat_start 2.45/1.45 2.45/1.45 leaf cost: 0 2.45/1.45 2.45/1.45 2.45/1.45 2.45/1.45 A polynomial rank function with 2.45/1.45 2.45/1.45 Pol(evalfoobb4in) = 1 2.45/1.45 2.45/1.45 Pol(evalfoobb1in) = 0 2.45/1.45 2.45/1.45 Pol(evalfoobb3in) = 2 2.45/1.45 2.45/1.45 Pol(evalfoobb2in) = 2 2.45/1.45 2.45/1.45 and size complexities 2.45/1.45 2.45/1.45 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 2.45/1.45 2.45/1.45 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 2.45/1.45 2.45/1.45 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 2.45/1.45 2.45/1.45 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ? 2.45/1.45 2.45/1.45 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-0) = ? 2.45/1.45 2.45/1.45 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4))", 0-0) = ? 2.45/1.45 2.45/1.45 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4))", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4))", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4))", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4))", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-0) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ]", 0-0) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ]", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\\ ar_4 >= 1 ]", 0-0) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\\ ar_4 >= 1 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\\ ar_4 >= 1 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\\ ar_4 >= 1 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\\ ar_4 >= 1 ]", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-0) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-0) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-4) = 1 2.45/1.45 2.45/1.45 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-0) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-2) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-4) = ar_4 2.45/1.45 2.45/1.45 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 2.45/1.45 2.45/1.45 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 2.45/1.45 2.45/1.45 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 2.45/1.45 2.45/1.45 orients the transitions 2.45/1.45 2.45/1.45 evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4)) 2.45/1.45 2.45/1.45 evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4)) 2.45/1.45 2.45/1.45 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ] 2.45/1.45 2.45/1.45 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.45/1.45 2.45/1.45 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\ ar_4 >= 1 ] 2.45/1.45 2.45/1.45 weakly and the transitions 2.45/1.45 2.45/1.45 evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4)) 2.45/1.45 2.45/1.45 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ] 2.45/1.45 2.45/1.45 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.45/1.45 2.45/1.45 strictly and produces the following problem: 2.45/1.45 2.45/1.45 5: T: 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: ar_1 + 1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\ ar_2 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\ ar_4 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ] 2.45/1.45 2.45/1.45 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4)) 2.45/1.45 2.45/1.45 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.45/1.45 2.45/1.45 start location: koat_start 2.45/1.45 2.45/1.45 leaf cost: 0 2.45/1.45 2.45/1.45 2.45/1.45 2.45/1.45 A polynomial rank function with 2.45/1.45 2.45/1.45 Pol(evalfoobb3in) = V_1 - 2*V_5 2.45/1.45 2.45/1.45 Pol(evalfoobb2in) = V_1 - V_5 2.45/1.45 2.45/1.45 and size complexities 2.45/1.45 2.45/1.45 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 2.45/1.45 2.45/1.45 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 2.45/1.45 2.45/1.45 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 2.45/1.45 2.45/1.45 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 3*ar_1 + 162 2.45/1.45 2.45/1.45 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-0) = 3*ar_1 + 18 2.45/1.45 2.45/1.45 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4))", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4))", 0-0) = 3*ar_1 + 18 2.45/1.45 2.45/1.45 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4))", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4))", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4))", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4))", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-0) = 3*ar_1 + 18 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ]", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ]", 0-0) = 3*ar_1 + 18 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ]", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\\ ar_4 >= 1 ]", 0-0) = 3*ar_1 + 18 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\\ ar_4 >= 1 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\\ ar_4 >= 1 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\\ ar_4 >= 1 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\\ ar_4 >= 1 ]", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-0) = 3*ar_1 + 54 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-0) = 3*ar_1 + 54 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-4) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-0) = 3*ar_1 + 18 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ? 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-4) = 1 2.45/1.45 2.45/1.45 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-0) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-2) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-4) = ar_4 2.45/1.45 2.45/1.45 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 2.45/1.45 2.45/1.45 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 2.45/1.45 2.45/1.45 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 2.45/1.45 2.45/1.45 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 2.45/1.45 2.45/1.45 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 2.45/1.45 2.45/1.45 orients the transitions 2.45/1.45 2.45/1.45 evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4)) 2.45/1.45 2.45/1.45 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\ ar_4 >= 1 ] 2.45/1.45 2.45/1.45 weakly and the transition 2.45/1.45 2.45/1.45 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\ ar_4 >= 1 ] 2.45/1.45 2.45/1.45 strictly and produces the following problem: 2.45/1.45 2.45/1.45 6: T: 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: ar_1 + 1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\ ar_2 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] 2.45/1.45 2.45/1.45 (Comp: 3*ar_1^2 + 22*ar_1 + 19, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\ ar_4 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ] 2.45/1.45 2.45/1.45 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.45/1.45 2.45/1.45 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4)) 2.45/1.45 2.45/1.45 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.45/1.45 2.45/1.45 start location: koat_start 2.45/1.45 2.45/1.45 leaf cost: 0 2.45/1.45 2.45/1.45 2.45/1.45 2.45/1.45 Repeatedly propagating knowledge in problem 6 produces the following problem: 2.45/1.45 2.45/1.45 7: T: 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: ar_1 + 1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_0 >= 0 /\ ar_2 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] 2.45/1.45 2.45/1.45 (Comp: 3*ar_1^2 + 22*ar_1 + 19, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 + 1 /\ ar_4 >= 1 ] 2.45/1.45 2.45/1.45 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 ] 2.45/1.45 2.45/1.45 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] 2.45/1.45 2.45/1.45 (Comp: 3*ar_1^2 + 22*ar_1 + 19, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, 2*ar_4)) 2.45/1.45 2.45/1.45 (Comp: 2*ar_1 + 2, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 2, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.45/1.45 2.45/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.45/1.45 2.45/1.45 start location: koat_start 2.45/1.45 2.45/1.45 leaf cost: 0 2.45/1.45 2.45/1.45 2.45/1.45 2.45/1.45 Complexity upper bound 51*ar_1 + 6*ar_1^2 + 53 2.45/1.45 2.45/1.45 2.45/1.45 2.45/1.45 Time: 0.190 sec (SMT: 0.150 sec) 2.45/1.45 2.45/1.45 2.45/1.45 ---------------------------------------- 2.45/1.45 2.45/1.45 (2) 2.45/1.45 BOUNDS(1, n^2) 2.48/2.78 EOF