/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^1)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 564 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_3, v_4, v_x, v_y)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: v_.0 > v_.01 && v_.01 >= 1 && v_.01 <= 2 eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: v_.0 <= v_.01 eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: v_.01 < 1 eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: v_.01 > 2 eval_foo_bb2_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_1(v_.0, v_.01, v_.0 - v_.01, v_4, v_x, v_y)) :|: TRUE eval_foo_1(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_3, v_4, v_x, v_y), eval_foo_2(v_.0, v_.01, v_3, nondef.0, v_x, v_y)) :|: TRUE eval_foo_2(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_3, v_4, v_3, v_4, v_x, v_y)) :|: TRUE eval_foo_.critedge_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: TRUE The start-symbols are:[eval_foo_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 36*ar_1 + 10) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ 2 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 3 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) (Comp: ?, Cost: 1) evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 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, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ 2 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 3 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) (Comp: ?, Cost: 1) evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 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(evalfoocritedgein) = 1 Pol(evalfoo1) = 2 Pol(evalfoo10) = 0 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoo11) = 2 Pol(evalfoo2) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 3 ] evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 ] evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ 2 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 3 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) (Comp: ?, Cost: 1) evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) (Comp: 2, Cost: 1) evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalfoo1: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ -X_3 + X_5 + 1 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 2 >= 0 /\ -X_3 + 2 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalfoo10: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 - 1 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ -X_3 + X_5 + 1 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 2 >= 0 /\ -X_3 + 2 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalfoo11: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 - 1 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ -X_3 + X_5 + 1 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 2 >= 0 /\ -X_3 + 2 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalfoo2: X_6 - X_7 >= 0 /\ -X_6 + X_7 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 - 1 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ -X_3 + X_5 + 1 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 2 >= 0 /\ -X_3 + 2 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalfoobb1in: -X_1 + X_2 >= 0 For symbol evalfoobb2in: -X_3 + 2 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalfoocritedgein: -X_1 + X_2 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6)) [ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 3 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ 2 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 6*V_2 Pol(evalfoostart) = 6*V_2 - 3 Pol(evalfoocritedgein) = 6*V_1 - 3 Pol(evalfoostop) = 6*V_1 - 3 Pol(evalfoo2) = 6*V_5 - 2 Pol(evalfoobb1in) = 6*V_1 - 3 Pol(evalfoo1) = 6*V_3 + 6*V_5 - 5 Pol(evalfoo10) = 1 Pol(evalfoo11) = 6*V_5 - 1 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoobb2in) = 6*V_1 - 4 Pol(evalfoobb0in) = 6*V_2 - 3 orients all transitions weakly and the transitions evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6)) [ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ 2 >= ar_2 ] evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 ] (Comp: 6*ar_1, Cost: 1) evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: 6*ar_1, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: 6*ar_1, Cost: 1) evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: 6*ar_1, Cost: 1) evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 + 1 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 2 >= 0 /\ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: 6*ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6)) [ -ar_2 + 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= 3 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_0 ] (Comp: 6*ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ 2 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) start location: koat_start leaf cost: 0 Complexity upper bound 36*ar_1 + 10 Time: 0.594 sec (SMT: 0.442 sec) ---------------------------------------- (2) BOUNDS(1, n^1)