/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^2)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 392 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.1, v_.13, v_r, v_x, v_y)) :|: TRUE eval_foo_bb0_in(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, -(v_x), -(v_y), v_r, v_x, v_y)) :|: v_x < 0 && v_y < 0 eval_foo_bb0_in(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, -(v_x), v_y, v_r, v_x, v_y)) :|: v_x < 0 && v_y >= 0 eval_foo_bb0_in(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_x, -(v_y), v_r, v_x, v_y)) :|: v_x >= 0 && v_y < 0 eval_foo_bb0_in(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_x, v_y, v_r, v_x, v_y)) :|: v_x >= 0 && v_y >= 0 eval_foo_bb1_in(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.1, v_.1, v_.13, v_r, v_x, v_y)) :|: v_.13 > 0 eval_foo_bb1_in(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.1, v_.13, v_r, v_x, v_y)) :|: v_.13 <= 0 eval_foo_bb2_in(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.1, v_.13, v_r, v_x, v_y)) :|: v_.0 >= v_.13 eval_foo_bb2_in(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.13, v_.0, v_r, v_x, v_y)) :|: v_.0 < v_.13 eval_foo_bb3_in(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0 - v_.13, v_.1, v_.13, v_r, v_x, v_y)) :|: TRUE eval_foo_bb4_in(v_.0, v_.1, v_.13, v_r, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.1, v_.13, v_r, v_x, v_y)) :|: TRUE The start-symbols are:[eval_foo_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 16*Ar_0*Ar_1 + 16*Ar_1^2 + 16*Ar_0 + 24*Ar_1 + 17) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\ 0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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(evalfoobb4in) = 1 Pol(evalfoobb3in) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb3in) = V_4 Pol(evalfoobb2in) = V_4 Pol(evalfoobb1in) = V_4 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3))", 0-0) = Ar_0 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3))", 0-1) = Ar_1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3))", 0-2) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3))", 0-3) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3))", 0-4) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ]", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ]", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ]", 0-2) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ]", 0-3) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ]", 0-4) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ]", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ]", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ]", 0-2) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ]", 0-3) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ]", 0-3) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ]", 0-3) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ]", 0-4) = ? S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-4) = Ar_4 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ] evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ] weakly and the transition evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: 4*Ar_1 + 4, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb3in) = 1 Pol(evalfoobb2in) = 1 Pol(evalfoobb1in) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3))", 0-0) = Ar_0 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3))", 0-1) = Ar_1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3))", 0-2) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3))", 0-3) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3))", 0-4) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ]", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ]", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ]", 0-2) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ]", 0-3) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ]", 0-4) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ]", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ]", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ]", 0-2) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ]", 0-3) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ]", 0-3) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ]", 0-3) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ]", 0-4) = ? S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-4) = Ar_4 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ] evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ] weakly and the transition evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: 4*Ar_1 + 4, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_3 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 ] (Comp: 4*Ar_1 + 4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_3 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol evalfoobb1in: X_3 + X_4 >= 0 /\ X_3 >= 0 For symbol evalfoobb2in: X_3 - X_5 >= 0 /\ X_4 + X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_3 >= 0 For symbol evalfoobb3in: X_3 - X_5 >= 0 /\ X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ -X_4 + X_5 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ X_3 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ X_3 - 1 >= 0 For symbol evalfoobb4in: -X_4 >= 0 /\ X_3 - X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_3 >= 0 This yielded the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_3 + Ar_4 - 2 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ Ar_2 - 1 >= 0 ] (Comp: 4*Ar_1 + 4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_3 + Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_3 + Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_4 >= Ar_3 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ 0 >= Ar_3 ] (Comp: 4*Ar_1 + 4, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb3in) = 2*V_5 - 1 Pol(evalfoobb2in) = 2*V_5 and size complexities S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 + 1 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-4) = Ar_4 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_3 >= 1 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_3 >= 1 ]", 0-2) = Ar_0 + Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_3 >= 1 ]", 0-3) = Ar_0 + Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_3 >= 1 ]", 0-4) = Ar_0 + Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ 0 >= Ar_3 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ 0 >= Ar_3 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ 0 >= Ar_3 ]", 0-2) = Ar_0 + Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ 0 >= Ar_3 ]", 0-3) = Ar_0 + Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ 0 >= Ar_3 ]", 0-4) = Ar_0 + Ar_1 + Ar_4 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_3 + Ar_4 - 1 >= 0 /\\ Ar_2 + Ar_4 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_4 >= Ar_3 ]", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_3 + Ar_4 - 1 >= 0 /\\ Ar_2 + Ar_4 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_4 >= Ar_3 ]", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_3 + Ar_4 - 1 >= 0 /\\ Ar_2 + Ar_4 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_4 >= Ar_3 ]", 0-2) = Ar_0 + Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_3 + Ar_4 - 1 >= 0 /\\ Ar_2 + Ar_4 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_4 >= Ar_3 ]", 0-3) = Ar_0 + Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_3 + Ar_4 - 1 >= 0 /\\ Ar_2 + Ar_4 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_4 >= Ar_3 ]", 0-4) = Ar_0 + Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_3 + Ar_4 - 1 >= 0 /\\ Ar_2 + Ar_4 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_3 >= Ar_4 + 1 ]", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_3 + Ar_4 - 1 >= 0 /\\ Ar_2 + Ar_4 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_3 >= Ar_4 + 1 ]", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_3 + Ar_4 - 1 >= 0 /\\ Ar_2 + Ar_4 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_3 >= Ar_4 + 1 ]", 0-2) = Ar_0 + Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_3 + Ar_4 - 1 >= 0 /\\ Ar_2 + Ar_4 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_3 >= Ar_4 + 1 ]", 0-3) = Ar_0 + Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_3 + Ar_4 - 1 >= 0 /\\ Ar_2 + Ar_4 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_3 >= Ar_4 + 1 ]", 0-4) = Ar_0 + Ar_1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_4 - 1 >= 0 /\\ Ar_3 + Ar_4 - 2 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 + Ar_4 - 2 >= 0 /\\ Ar_2 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ Ar_2 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_4 - 1 >= 0 /\\ Ar_3 + Ar_4 - 2 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 + Ar_4 - 2 >= 0 /\\ Ar_2 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ Ar_2 - 1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_4 - 1 >= 0 /\\ Ar_3 + Ar_4 - 2 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 + Ar_4 - 2 >= 0 /\\ Ar_2 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ Ar_2 - 1 >= 0 ]", 0-2) = Ar_0 + Ar_1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_4 - 1 >= 0 /\\ Ar_3 + Ar_4 - 2 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 + Ar_4 - 2 >= 0 /\\ Ar_2 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ Ar_2 - 1 >= 0 ]", 0-3) = Ar_0 + Ar_1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) [ Ar_2 - Ar_4 >= 0 /\\ Ar_4 - 1 >= 0 /\\ Ar_3 + Ar_4 - 2 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 + Ar_4 - 2 >= 0 /\\ Ar_2 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ Ar_2 - 1 >= 0 ]", 0-4) = Ar_0 + Ar_1 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 >= 0 /\\ Ar_2 - Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 ]", 0-0) = Ar_0 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 >= 0 /\\ Ar_2 - Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 ]", 0-1) = Ar_1 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 >= 0 /\\ Ar_2 - Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 ]", 0-2) = Ar_0 + Ar_1 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 >= 0 /\\ Ar_2 - Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 ]", 0-3) = Ar_0 + Ar_1 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 >= 0 /\\ Ar_2 - Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 ]", 0-4) = Ar_0 + Ar_1 + Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 orients the transitions evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_3 + Ar_4 - 2 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ Ar_2 - 1 >= 0 ] evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_3 + Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_4 >= Ar_3 ] weakly and the transitions evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_3 + Ar_4 - 2 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ Ar_2 - 1 >= 0 ] evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_3 + Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_4 >= Ar_3 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 ] (Comp: 8*Ar_0*Ar_1 + 8*Ar_1^2 + 8*Ar_0 + 8*Ar_1, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - Ar_3)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_3 + Ar_4 - 2 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ Ar_2 - 1 >= 0 ] (Comp: 4*Ar_1 + 4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_4, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_3 + Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= Ar_4 + 1 ] (Comp: 8*Ar_0*Ar_1 + 8*Ar_1^2 + 8*Ar_0 + 8*Ar_1, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_3 + Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_4 >= Ar_3 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ 0 >= Ar_3 ] (Comp: 4*Ar_1 + 4, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, -Ar_1, Ar_4)) [ Ar_0 >= 0 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, -Ar_0, -Ar_1, Ar_4)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 Complexity upper bound 16*Ar_0*Ar_1 + 16*Ar_1^2 + 16*Ar_0 + 24*Ar_1 + 17 Time: 0.327 sec (SMT: 0.259 sec) ---------------------------------------- (2) BOUNDS(1, n^2)