/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 783 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_tx, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_3, v_tx, v_x, v_y)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_3, v_tx, v_x, v_y)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_3, v_tx, v_x, v_y)) :|: v_.0 >= v_.01 && v_tx >= 0 eval_foo_bb1_in(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_3, v_tx, v_x, v_y)) :|: v_.0 < v_.01 eval_foo_bb1_in(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_3, v_tx, v_x, v_y)) :|: v_tx < 0 eval_foo_bb2_in(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_0(v_.0, v_.01, v_3, v_tx, v_x, v_y)) :|: TRUE eval_foo_0(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_3, v_tx, v_x, v_y), eval_foo_1(v_.0, v_.01, nondef.0, v_tx, v_x, v_y)) :|: TRUE eval_foo_1(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_3, v_tx, v_x, v_y)) :|: v_3 < 0 eval_foo_1(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_3, v_tx, v_x, v_y)) :|: v_3 > 0 eval_foo_1(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_3, v_tx, v_x, v_y)) :|: v_3 >= 0 && v_3 <= 0 eval_foo_bb3_in(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - v_tx - 1, v_.01, v_3, v_tx, v_x, v_y)) :|: TRUE eval_foo_bb4_in(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 + v_tx + 1, v_3, v_tx, v_x, v_y)) :|: TRUE eval_foo_bb5_in(v_.0, v_.01, v_3, v_tx, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_3, v_tx, v_x, v_y)) :|: TRUE The start-symbols are:[eval_foo_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 70*ar_1 + 70*ar_3 + 78) 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 /\ ar_4 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoo00(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) evalfoo01(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_4, ar_6, ar_6)) (Comp: ?, Cost: 1) evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_5 + 1 ] (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= 1 ] (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 = 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0 - ar_4 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + ar_4 + 1, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoobb5in(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 /\ ar_4 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoo00(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) evalfoo01(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_4, ar_6, ar_6)) (Comp: ?, Cost: 1) evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_5 + 1 ] (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= 1 ] (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 = 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0 - ar_4 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + ar_4 + 1, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoobb5in(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(evalfoobb5in) = 1 Pol(evalfoo0) = 2 Pol(evalfoo00) = 0 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoo01) = 2 Pol(evalfoo1) = 2 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, 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(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 + 1 ] evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_4 + 1 ] 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 /\ ar_4 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoo00(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) evalfoo01(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_4, ar_6, ar_6)) (Comp: ?, Cost: 1) evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_5 + 1 ] (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= 1 ] (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 = 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0 - ar_4 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + ar_4 + 1, ar_3, ar_4, ar_5, ar_6)) (Comp: 2, Cost: 1) evalfoobb5in(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 evalfoo0: X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_2 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoo00: X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_2 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoo01: X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_2 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoo1: X_6 - X_7 >= 0 /\ -X_6 + X_7 >= 0 /\ X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_2 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb1in: X_3 - X_4 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb2in: X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_2 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb3in: X_6 - X_7 >= 0 /\ -X_6 + X_7 >= 0 /\ X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_2 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb4in: -X_7 >= 0 /\ X_6 - X_7 >= 0 /\ -X_6 - X_7 >= 0 /\ X_5 - X_7 >= 0 /\ X_7 >= 0 /\ X_6 + X_7 >= 0 /\ -X_6 + X_7 >= 0 /\ X_5 + X_7 >= 0 /\ -X_6 >= 0 /\ X_5 - X_6 >= 0 /\ X_6 >= 0 /\ X_5 + X_6 >= 0 /\ X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_2 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb5in: X_3 - X_4 >= 0 /\ -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) evalfoobb5in(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_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + ar_4 + 1, ar_3, ar_4, ar_5, ar_6)) [ -ar_6 >= 0 /\ ar_5 - ar_6 >= 0 /\ -ar_5 - ar_6 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_6 >= 0 /\ ar_5 + ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 + ar_6 >= 0 /\ -ar_5 >= 0 /\ ar_4 - ar_5 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0 - ar_4 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_5 = 0 ] (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_5 >= 1 ] (Comp: ?, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_5 + 1 ] (Comp: ?, Cost: 1) evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoo01(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_4, ar_6, ar_6)) [ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoo00(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_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ] (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_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= ar_2 /\ ar_4 >= 0 ] (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) = 7*V_2 - 7*V_4 + 7 Pol(evalfoostart) = 7*V_2 - 7*V_4 + 7 Pol(evalfoobb5in) = 7*V_1 - 7*V_3 Pol(evalfoostop) = 7*V_1 - 7*V_3 Pol(evalfoobb4in) = 7*V_1 - 7*V_3 + 1 Pol(evalfoobb1in) = 7*V_1 - 7*V_3 + 7 Pol(evalfoobb3in) = 7*V_1 - 7*V_3 + 1 Pol(evalfoo1) = 7*V_1 - 7*V_3 + 2 Pol(evalfoo0) = 7*V_1 - 7*V_3 + 5 Pol(evalfoo00) = 1 Pol(evalfoo01) = 7*V_1 - 7*V_3 + 3 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoobb2in) = 7*V_1 - 7*V_3 + 6 Pol(evalfoobb0in) = 7*V_2 - 7*V_4 + 7 orients all transitions weakly and the transitions evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + ar_4 + 1, ar_3, ar_4, ar_5, ar_6)) [ -ar_6 >= 0 /\ ar_5 - ar_6 >= 0 /\ -ar_5 - ar_6 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_6 >= 0 /\ ar_5 + ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 + ar_6 >= 0 /\ -ar_5 >= 0 /\ ar_4 - ar_5 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0 - ar_4 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 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_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= ar_2 /\ ar_4 >= 0 ] evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_5 = 0 ] evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_5 >= 1 ] evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_5 + 1 ] evalfoo01(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_4, ar_6, ar_6)) [ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] evalfoo00(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_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 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) evalfoobb5in(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_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: 7*ar_1 + 7*ar_3 + 7, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + ar_4 + 1, ar_3, ar_4, ar_5, ar_6)) [ -ar_6 >= 0 /\ ar_5 - ar_6 >= 0 /\ -ar_5 - ar_6 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_6 >= 0 /\ ar_5 + ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 + ar_6 >= 0 /\ -ar_5 >= 0 /\ ar_4 - ar_5 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: 7*ar_1 + 7*ar_3 + 7, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_0 - ar_4 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: 7*ar_1 + 7*ar_3 + 7, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_5 = 0 ] (Comp: 7*ar_1 + 7*ar_3 + 7, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_5 >= 1 ] (Comp: 7*ar_1 + 7*ar_3 + 7, Cost: 1) evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_5 + 1 ] (Comp: 7*ar_1 + 7*ar_3 + 7, Cost: 1) evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: 7*ar_1 + 7*ar_3 + 7, Cost: 1) evalfoo01(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_4, ar_6, ar_6)) [ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: 7*ar_1 + 7*ar_3 + 7, Cost: 1) evalfoo00(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_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: 7*ar_1 + 7*ar_3 + 7, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ] (Comp: 7*ar_1 + 7*ar_3 + 7, 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_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= ar_2 /\ ar_4 >= 0 ] (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 70*ar_1 + 70*ar_3 + 78 Time: 0.786 sec (SMT: 0.605 sec) ---------------------------------------- (2) BOUNDS(1, n^1)