/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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_5, v_oldx, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_5, v_oldx, v_x)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_5, v_oldx, v_x) -> Com_1(eval_foo_bb1_in(v_x, v_oldx, v_5, v_oldx, v_x)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_5, v_oldx, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_5, v_oldx, v_x)) :|: v_.0 > 0 && v_.0 < 100 eval_foo_bb1_in(v_.0, v_.01, v_5, v_oldx, v_x) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_5, v_oldx, v_x)) :|: v_.0 <= 0 eval_foo_bb1_in(v_.0, v_.01, v_5, v_oldx, v_x) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_5, v_oldx, v_x)) :|: v_.0 >= 100 eval_foo_bb2_in(v_.0, v_.01, v_5, v_oldx, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_5, v_oldx, v_x)) :|: v_.0 >= 2 * v_.01 + 10 eval_foo_bb2_in(v_.0, v_.01, v_5, v_oldx, v_x) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_5, v_oldx, v_x)) :|: v_.0 < 2 * v_.01 + 10 eval_foo_bb3_in(v_.0, v_.01, v_5, v_oldx, v_x) -> Com_1(eval_foo_3(v_.0, v_.01, v_5, v_oldx, v_x)) :|: TRUE eval_foo_3(v_.0, v_.01, v_5, v_oldx, v_x) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_5, v_oldx, v_x), eval_foo_4(v_.0, v_.01, nondef.0, v_oldx, v_x)) :|: TRUE eval_foo_4(v_.0, v_.01, v_5, v_oldx, v_x) -> Com_1(eval_foo_bb1_in(v_5, v_.0, v_5, v_oldx, v_x)) :|: TRUE eval_foo_.critedge_in(v_.0, v_.01, v_5, v_oldx, v_x) -> Com_1(eval_foo_stop(v_.0, v_.01, v_5, v_oldx, v_x)) :|: TRUE The start-symbols are:[eval_foo_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 5516*Ar_3 + 546704) 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 /\ 99 >= 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)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2*Ar_2 + 10 ] (Comp: ?, Cost: 1) evalfoobb2in(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_2 + 9 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoo30(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) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) (Comp: ?, Cost: 1) evalfoo4(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 /\ 99 >= 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)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2*Ar_2 + 10 ] (Comp: ?, Cost: 1) evalfoobb2in(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_2 + 9 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoo30(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) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) (Comp: ?, Cost: 1) evalfoo4(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(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) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfoobb2in(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_2 + 9 >= Ar_0 ] 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_0 >= 100 ] 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 /\ 99 >= 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)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2*Ar_2 + 10 ] (Comp: 2, Cost: 1) evalfoobb2in(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_2 + 9 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoo30(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) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) (Comp: ?, Cost: 1) evalfoo4(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 evalfoo3: -X_3 + 44 >= 0 /\ X_1 - X_3 + 43 >= 0 /\ -X_1 - X_3 + 143 >= 0 /\ -X_1 + 99 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo30: -X_3 + 44 >= 0 /\ X_1 - X_3 + 43 >= 0 /\ -X_1 - X_3 + 143 >= 0 /\ -X_1 + 99 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo31: -X_3 + 44 >= 0 /\ X_1 - X_3 + 43 >= 0 /\ -X_1 - X_3 + 143 >= 0 /\ -X_1 + 99 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo4: X_5 - X_6 >= 0 /\ -X_5 + X_6 >= 0 /\ -X_3 + 44 >= 0 /\ X_1 - X_3 + 43 >= 0 /\ -X_1 - X_3 + 143 >= 0 /\ -X_1 + 99 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb2in: -X_1 + 99 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb3in: -X_3 + 44 >= 0 /\ X_1 - X_3 + 43 >= 0 /\ -X_1 - X_3 + 143 >= 0 /\ -X_1 + 99 >= 0 /\ X_1 - 1 >= 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)) (Comp: ?, Cost: 1) evalfoo4(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_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(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_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb2in(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_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 /\ 2*Ar_2 + 9 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= 2*Ar_2 + 10 ] (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_0 >= 100 ] (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: ?, 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 /\ 99 >= 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) = -788*V_4 + 78099 Pol(evalfoostart) = -788*V_4 + 78099 Pol(evalfoocritedgein) = -788*V_3 + 78099 Pol(evalfoostop) = -788*V_3 Pol(evalfoo4) = -788*V_1 - 22*V_3 + 79078 Pol(evalfoobb1in) = -788*V_3 + 78099 Pol(evalfoo3) = -383*V_1 - 22*V_3 + 81907 Pol(evalfoo30) = 1078 Pol(evalfoo31) = -788*V_1 - 22*V_3 + 80156 Pol(evalVERIFIERnondetintstart) = 1077 Pol(evalfoobb3in) = -383*V_1 - 22*V_3 + 81918 Pol(evalfoobb2in) = -788*V_3 + 78099 Pol(evalfoobb0in) = -788*V_4 + 78099 orients all transitions weakly and the transitions evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= 2*Ar_2 + 10 ] evalfoo4(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_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoo30(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_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 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)) (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoo4(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_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoo30(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_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb2in(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_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 /\ 2*Ar_2 + 9 >= Ar_0 ] (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= 2*Ar_2 + 10 ] (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_0 >= 100 ] (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: ?, 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 /\ 99 >= 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 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: 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)) (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoo4(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_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_5, Ar_5)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoo30(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_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + 44 >= 0 /\ Ar_0 - Ar_2 + 43 >= 0 /\ -Ar_0 - Ar_2 + 143 >= 0 /\ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb2in(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_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 /\ 2*Ar_2 + 9 >= Ar_0 ] (Comp: 788*Ar_3 + 78099, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_0 + 99 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= 2*Ar_2 + 10 ] (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_0 >= 100 ] (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: 788*Ar_3 + 78100, 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 /\ 99 >= 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 5516*Ar_3 + 546704 Time: 0.361 sec (SMT: 0.273 sec) ---------------------------------------- (2) BOUNDS(1, n^1)