/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^3)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). (0) CpxIntTrs (1) Koat Proof [FINISHED, 185 ms] (2) BOUNDS(1, n^3) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= 0 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < 0 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + v_.01, v_.01 - 1, v_x, v_y)) :|: v_.01 >= 0 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + v_.01, v_.01, v_x, v_y)) :|: v_.01 < 0 eval_foo_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE The start-symbols are:[eval_foo_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 8*Ar_1 + 4*Ar_1*Ar_3 + 16*Ar_3^2 + 4*Ar_3^3 + 25*Ar_3 + 23) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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(evalfoobb3in) = 1 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = V_4 + 1 Pol(evalfoobb0in) = V_4 + 1 Pol(evalfoobb1in) = V_3 + 1 Pol(evalfoobb2in) = V_3 + 1 Pol(evalfoobb3in) = V_3 Pol(evalfoostop) = V_3 Pol(koat_start) = V_4 + 1 orients all transitions weakly and the transition evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: Ar_3 + 1, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 4 to obtain the following invariants: For symbol evalfoobb1in: -X_3 + X_4 >= 0 For symbol evalfoobb2in: -X_3 + X_4 >= 0 /\ X_1 >= 0 For symbol evalfoobb3in: -X_3 + X_4 >= 0 /\ -X_1 - 1 >= 0 This yielded the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 + 1 ] (Comp: Ar_3 + 1, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb2in) = 2*V_1 + 1 Pol(evalfoobb1in) = 2*V_1 + 2 and size complexities S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3))", 0-0) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3))", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3))", 0-2) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3))", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_1 + 3*Ar_3 + Ar_3^2 + 2 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_3 + 1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-0) = Ar_1 + 3*Ar_3 + Ar_3^2 + 2 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-2) = Ar_3 + 1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 0 ]", 0-0) = Ar_1 + 3*Ar_3 + Ar_3^2 + 2 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 0 ]", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 0 ]", 0-2) = Ar_3 + 1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 0 ]", 0-3) = Ar_3 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-0) = Ar_1 + 3*Ar_3 + Ar_3^2 + 2 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-2) = Ar_3 + 1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-3) = Ar_3 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ -Ar_0 - 1 >= 0 ]", 0-0) = Ar_1 + 3*Ar_3 + Ar_3^2 + 2 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ -Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ -Ar_0 - 1 >= 0 ]", 0-2) = Ar_3 + 1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\\ -Ar_0 - 1 >= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 + 1 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 0 ] weakly and the transitions evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 + 1 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 - 1 >= 0 ] (Comp: 4*Ar_1 + 2*Ar_1*Ar_3 + 8*Ar_3^2 + 2*Ar_3^3 + 12*Ar_3 + 8, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 + 1 ] (Comp: Ar_3 + 1, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0 + Ar_2, Ar_1, Ar_2 - 1, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 4*Ar_1 + 2*Ar_1*Ar_3 + 8*Ar_3^2 + 2*Ar_3^3 + 12*Ar_3 + 8, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 8*Ar_1 + 4*Ar_1*Ar_3 + 16*Ar_3^2 + 4*Ar_3^3 + 25*Ar_3 + 23 Time: 0.217 sec (SMT: 0.180 sec) ---------------------------------------- (2) BOUNDS(1, n^3)