/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 289 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_oldx, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_3, v_oldx, v_x)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_bb1_in(v_x, v_oldx, v_3, v_oldx, v_x)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_3, v_oldx, v_x)) :|: v_.0 > 0 && 2 * v_.0 <= v_.01 eval_foo_bb1_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_3, v_oldx, v_x)) :|: v_.0 <= 0 eval_foo_bb1_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_3, v_oldx, v_x)) :|: 2 * v_.0 > v_.01 eval_foo_bb2_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_2(v_.0, v_.01, v_3, v_oldx, v_x)) :|: TRUE eval_foo_2(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_3, v_oldx, v_x), eval_foo_3(v_.0, v_.01, nondef.0, v_oldx, v_x)) :|: TRUE eval_foo_3(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_bb1_in(v_3, v_.0, v_3, v_oldx, v_x)) :|: TRUE eval_foo_.critedge_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_stop(v_.0, v_.01, v_3, v_oldx, v_x)) :|: TRUE The start-symbols are:[eval_foo_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 36*Ar_3 + 8) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_2 >= 2*Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 2*Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_0, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_2 >= 2*Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 2*Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_0, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 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(evalfoo2) = 2 Pol(evalfoo20) = 0 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoo21) = 2 Pol(evalfoo3) = 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) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 2*Ar_0 >= Ar_2 + 1 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 ] 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_2 >= 2*Ar_0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 2*Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_0, Ar_3, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalfoo2: X_4 - 2 >= 0 /\ X_3 + X_4 - 4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_3 - 2 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo20: X_4 - 2 >= 0 /\ X_3 + X_4 - 4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_3 - 2 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo21: X_4 - 2 >= 0 /\ X_3 + X_4 - 4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_3 - 2 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo3: X_5 - X_6 >= 0 /\ -X_5 + X_6 >= 0 /\ X_4 - 2 >= 0 /\ X_3 + X_4 - 4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_3 - 2 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb1in: -X_3 + X_4 >= 0 For symbol evalfoobb2in: X_4 - 2 >= 0 /\ X_3 + X_4 - 4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_3 - 2 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoocritedgein: -X_3 + X_4 >= 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) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_4 - Ar_5 >= 0 /\ -Ar_4 + Ar_5 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_3 >= 0 /\ 2*Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_3 >= 0 /\ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 1 /\ Ar_2 >= 2*Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 6*V_4 Pol(evalfoostart) = 6*V_4 Pol(evalfoocritedgein) = 6*V_3 Pol(evalfoostop) = 6*V_3 Pol(evalfoo3) = 6*V_1 + 1 Pol(evalfoobb1in) = 6*V_3 Pol(evalfoo2) = 10*V_1 Pol(evalfoo20) = 4*V_1 - 3 Pol(evalfoo21) = 6*V_1 + 2 Pol(evalVERIFIERnondetintstart) = 4*V_1 - 4 Pol(evalfoobb2in) = 12*V_1 - 1 Pol(evalfoobb0in) = 6*V_4 orients all transitions weakly and the transitions evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 1 /\ Ar_2 >= 2*Ar_0 ] evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_4 - Ar_5 >= 0 /\ -Ar_4 + Ar_5 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 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) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_3 >= 0 ] (Comp: 6*Ar_3, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_4 - Ar_5 >= 0 /\ -Ar_4 + Ar_5 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 6*Ar_3, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 6*Ar_3, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 6*Ar_3, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 6*Ar_3, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_3 >= 0 /\ 2*Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_3 >= 0 /\ 0 >= Ar_0 ] (Comp: 6*Ar_3, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_3 >= 0 /\ Ar_0 >= 1 /\ Ar_2 >= 2*Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 Complexity upper bound 36*Ar_3 + 8 Time: 0.254 sec (SMT: 0.187 sec) ---------------------------------------- (2) BOUNDS(1, n^1)