/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 878 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_oldy, v_3, v_oldy, v_x, v_y)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y)) :|: v_.0 > 0 eval_foo_bb1_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y)) :|: v_.0 <= 0 eval_foo_bb2_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y)) :|: v_.01 <= -(v_.02) eval_foo_bb2_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y)) :|: v_.01 > -(v_.02) eval_foo_bb3_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y) -> Com_1(eval_foo_2(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y)) :|: TRUE eval_foo_2(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y), eval_foo_3(v_.0, v_.01, v_.02, nondef.0, v_oldy, v_x, v_y)) :|: TRUE eval_foo_3(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_3, v_.01, v_3, v_oldy, v_x, v_y)) :|: TRUE eval_foo_.critedge_in(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.02, v_3, v_oldy, v_x, v_y)) :|: TRUE The start-symbols are:[eval_foo_start_7] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 31) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_4 + Ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_7, Ar_7)) (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_6, Ar_3, Ar_2, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 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, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_4 + Ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_7, Ar_7)) (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_6, Ar_3, Ar_2, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 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(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, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 + Ar_4 >= 1 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 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, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_4 + Ar_2 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_7, Ar_7)) (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_6, Ar_3, Ar_2, Ar_5, Ar_6, Ar_7)) (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 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_3 - X_5 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo20: -X_3 - X_5 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo21: -X_3 - X_5 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo3: X_7 - X_8 >= 0 /\ -X_7 + X_8 >= 0 /\ -X_3 - X_5 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb2in: X_1 - 1 >= 0 For symbol evalfoobb3in: -X_3 - X_5 >= 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, Ar_6, Ar_7) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_6, Ar_3, Ar_2, Ar_5, Ar_6, Ar_7)) [ Ar_6 - Ar_7 >= 0 /\ -Ar_6 + Ar_7 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) start location: koat_start leaf cost: 0 By chaining the transition koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained: koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] We thus obtain the following problem: 5: T: (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_6, Ar_3, Ar_2, Ar_5, Ar_6, Ar_7)) [ Ar_6 - Ar_7 >= 0 /\ -Ar_6 + Ar_7 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 5: evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) We thus obtain the following problem: 6: T: (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_6, Ar_3, Ar_2, Ar_5, Ar_6, Ar_7)) [ Ar_6 - Ar_7 >= 0 /\ -Ar_6 + Ar_7 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] with all transitions in problem 6, the following new transition is obtained: evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] We thus obtain the following problem: 7: T: (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_6, Ar_3, Ar_2, Ar_5, Ar_6, Ar_7)) [ Ar_6 - Ar_7 >= 0 /\ -Ar_6 + Ar_7 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 7: evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_6, Ar_3, Ar_2, Ar_5, Ar_6, Ar_7)) [ Ar_6 - Ar_7 >= 0 /\ -Ar_6 + Ar_7 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] We thus obtain the following problem: 8: T: (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] with all transitions in problem 8, the following new transition is obtained: evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] We thus obtain the following problem: 9: T: (Comp: ?, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 9: evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] We thus obtain the following problem: 10: T: (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 ] with all transitions in problem 10, the following new transition is obtained: evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] We thus obtain the following problem: 11: T: (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 11: evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] We thus obtain the following problem: 12: T: (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] with all transitions in problem 12, the following new transition is obtained: evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] We thus obtain the following problem: 13: T: (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] with all transitions in problem 13, the following new transition is obtained: evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] We thus obtain the following problem: 14: T: (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 14: evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) We thus obtain the following problem: 15: T: (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] with all transitions in problem 15, the following new transition is obtained: koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] We thus obtain the following problem: 16: T: (Comp: 1, Cost: 2) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 16: evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) We thus obtain the following problem: 17: T: (Comp: ?, Cost: 2) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 2) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 ] with all transitions in problem 17, the following new transitions are obtained: evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ 0 >= Ar_2 ] evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 ] We thus obtain the following problem: 18: T: (Comp: ?, Cost: 4) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ 0 >= Ar_2 ] (Comp: ?, Cost: 3) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 2) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 18 produces the following problem: 19: T: (Comp: ?, Cost: 4) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ 0 >= Ar_2 ] (Comp: ?, Cost: 3) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 2) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoo21) = 1 Pol(evalfoostop) = 0 Pol(evalfoobb2in) = 1 Pol(evalfoo20) = 0 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoobb1in) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ 0 >= Ar_2 ] strictly and produces the following problem: 20: T: (Comp: 1, Cost: 4) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ 0 >= Ar_2 ] (Comp: ?, Cost: 3) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 2) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 ] with all transitions in problem 20, the following new transitions are obtained: evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 /\ Ar_2 - 1 >= 0 /\ Ar_7 + Ar_2 >= 1 ] evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Fresh_0), evalfoo21(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 /\ Ar_2 - 1 >= 0 /\ 0 >= Ar_2 + Ar_7 /\ -Ar_7 - Ar_2 >= 0 ] We thus obtain the following problem: 21: T: (Comp: ?, Cost: 5) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 /\ Ar_2 - 1 >= 0 /\ Ar_7 + Ar_2 >= 1 ] (Comp: ?, Cost: 6) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Fresh_0), evalfoo21(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 /\ Ar_2 - 1 >= 0 /\ 0 >= Ar_2 + Ar_7 /\ -Ar_7 - Ar_2 >= 0 ] (Comp: 1, Cost: 4) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 2) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 21 produces the following problem: 22: T: (Comp: 1, Cost: 5) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 /\ Ar_2 - 1 >= 0 /\ Ar_7 + Ar_2 >= 1 ] (Comp: 1, Cost: 6) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Fresh_0), evalfoo21(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Fresh_0)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ Ar_2 >= 1 /\ Ar_2 - 1 >= 0 /\ 0 >= Ar_2 + Ar_7 /\ -Ar_7 - Ar_2 >= 0 ] (Comp: 1, Cost: 4) evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_2, Ar_1, Ar_7, Ar_3, Ar_2, Ar_5, Ar_7, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= 0 /\ 0 >= Ar_2 ] (Comp: 2, Cost: 1) evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ -Ar_2 - Ar_4 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 - 1 >= 0 /\ Ar_2 + Ar_4 >= 1 ] (Comp: 1, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_2(evalfoo20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0), evalfoo21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_0)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_4 + Ar_2 /\ -Ar_2 - Ar_4 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 2) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 31 Time: 0.840 sec (SMT: 0.573 sec) ---------------------------------------- (2) BOUNDS(1, 1)