/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 381 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_tmp, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x) -> Com_1(eval_foo_bb1_in(v_x, v_tmp, v_3, v_4, v_tmp, v_x)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x)) :|: v_.0 > 0 eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x)) :|: v_.0 <= 0 eval_foo_bb2_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x)) :|: v_.0 >= 2 * v_.01 && v_.0 <= 2 * v_.01 eval_foo_bb2_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x)) :|: v_.0 < 2 * v_.01 eval_foo_bb2_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x)) :|: v_.0 > 2 * v_.01 eval_foo_bb3_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x) -> Com_1(eval_foo_3(v_.0, v_.01, v_.0 - 1, v_4, v_tmp, v_x)) :|: TRUE eval_foo_3(v_.0, v_.01, v_3, v_4, v_tmp, v_x) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_3, v_4, v_tmp, v_x), eval_foo_4(v_.0, v_.01, v_3, nondef.0, v_tmp, v_x)) :|: TRUE eval_foo_4(v_.0, v_.01, v_3, v_4, v_tmp, v_x) -> Com_1(eval_foo_bb1_in(v_3, v_4, v_3, v_4, v_tmp, v_x)) :|: TRUE eval_foo_.critedge_in(v_.0, v_.01, v_3, v_4, v_tmp, v_x) -> Com_1(eval_foo_stop(v_.0, v_.01, v_3, v_4, v_tmp, v_x)) :|: TRUE The start-symbols are:[eval_foo_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 98*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 >= 1 ] (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_0 ] (Comp: ?, Cost: 1) evalfoobb2in(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_0 = 2*Ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(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)) [ 2*Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(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 >= 2*Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoo30(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) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_6, Ar_6)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) (Comp: ?, Cost: 1) evalfoo4(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 >= 1 ] (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_0 ] (Comp: ?, Cost: 1) evalfoobb2in(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_0 = 2*Ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(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)) [ 2*Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(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 >= 2*Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoo30(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) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_6, Ar_6)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) (Comp: ?, Cost: 1) evalfoo4(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(evalfoobb3in) = 2 Pol(evalfoo3) = 2 Pol(evalfoo30) = 0 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoo31) = 2 Pol(evalfoo4) = 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)) evalfoobb2in(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)) [ 2*Ar_2 >= Ar_0 + 1 ] evalfoobb2in(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 >= 2*Ar_2 + 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_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, 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 >= 1 ] (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_0 ] (Comp: ?, Cost: 1) evalfoobb2in(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_0 = 2*Ar_2 ] (Comp: 2, Cost: 1) evalfoobb2in(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)) [ 2*Ar_2 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalfoobb2in(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 >= 2*Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoo30(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) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_6, Ar_6)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) (Comp: ?, Cost: 1) evalfoo4(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 evalfoo3: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 - 1 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 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 evalfoo30: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 - 1 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 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 evalfoo31: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 - 1 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 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 evalfoo4: 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_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 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_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb3in: 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) evalfoo4(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_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo4(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_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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) evalfoo30(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_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) [ 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) evalfoobb2in(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_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= 2*Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfoobb2in(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_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ 2*Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(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_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 = 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_0 + Ar_1 >= 0 /\ 0 >= 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 >= 1 ] (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) = 14*V_2 Pol(evalfoostart) = 14*V_2 - 11 Pol(evalfoocritedgein) = 14*V_1 - 13 Pol(evalfoostop) = 14*V_1 - 13 Pol(evalfoo4) = 14*V_5 - 9 Pol(evalfoobb1in) = 14*V_1 - 11 Pol(evalfoo3) = -3*V_1 + 17*V_5 Pol(evalfoo30) = 2 Pol(evalfoo31) = 14*V_5 - 7 Pol(evalVERIFIERnondetintstart) = 1 Pol(evalfoobb3in) = 14*V_1 - 15 Pol(evalfoobb2in) = 14*V_1 - 13 Pol(evalfoobb0in) = 14*V_2 - 11 orients all transitions weakly and the transitions evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) [ 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 ] evalfoobb2in(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_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 = 2*Ar_2 ] 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 >= 1 ] evalfoo4(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_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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 ] evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo4(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_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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 ] evalfoo30(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_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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 ] evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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: 14*Ar_1, Cost: 1) evalfoo4(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_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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: 14*Ar_1, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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: 14*Ar_1, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo4(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_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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: 14*Ar_1, Cost: 1) evalfoo30(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_1 + Ar_4 - 3 >= 0 /\ Ar_0 + Ar_4 - 3 >= 0 /\ -Ar_0 + Ar_4 + 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: 14*Ar_1, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) [ 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) evalfoobb2in(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_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= 2*Ar_2 + 1 ] (Comp: 2, Cost: 1) evalfoobb2in(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_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ 2*Ar_2 >= Ar_0 + 1 ] (Comp: 14*Ar_1, Cost: 1) evalfoobb2in(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_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 = 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_0 + Ar_1 >= 0 /\ 0 >= Ar_0 ] (Comp: 14*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 >= 1 ] (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 98*Ar_1 + 10 Time: 0.391 sec (SMT: 0.268 sec) ---------------------------------------- (2) BOUNDS(1, n^1)