/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 179 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speedpldi2_start(v_m, v_n, v_v1.0, v_v2.0) -> Com_1(eval_speedpldi2_bb0_in(v_m, v_n, v_v1.0, v_v2.0)) :|: TRUE eval_speedpldi2_bb0_in(v_m, v_n, v_v1.0, v_v2.0) -> Com_1(eval_speedpldi2_bb1_in(v_m, v_n, v_n, 0)) :|: v_n >= 0 && v_m > 0 eval_speedpldi2_bb0_in(v_m, v_n, v_v1.0, v_v2.0) -> Com_1(eval_speedpldi2_bb4_in(v_m, v_n, v_v1.0, v_v2.0)) :|: v_n < 0 eval_speedpldi2_bb0_in(v_m, v_n, v_v1.0, v_v2.0) -> Com_1(eval_speedpldi2_bb4_in(v_m, v_n, v_v1.0, v_v2.0)) :|: v_m <= 0 eval_speedpldi2_bb1_in(v_m, v_n, v_v1.0, v_v2.0) -> Com_1(eval_speedpldi2_bb2_in(v_m, v_n, v_v1.0, v_v2.0)) :|: v_v1.0 > 0 eval_speedpldi2_bb1_in(v_m, v_n, v_v1.0, v_v2.0) -> Com_1(eval_speedpldi2_bb4_in(v_m, v_n, v_v1.0, v_v2.0)) :|: v_v1.0 <= 0 eval_speedpldi2_bb2_in(v_m, v_n, v_v1.0, v_v2.0) -> Com_1(eval_speedpldi2_bb3_in(v_m, v_n, v_v1.0, v_v2.0)) :|: v_v2.0 < v_m eval_speedpldi2_bb2_in(v_m, v_n, v_v1.0, v_v2.0) -> Com_1(eval_speedpldi2_bb1_in(v_m, v_n, v_v1.0, 0)) :|: v_v2.0 >= v_m eval_speedpldi2_bb3_in(v_m, v_n, v_v1.0, v_v2.0) -> Com_1(eval_speedpldi2_bb1_in(v_m, v_n, v_v1.0 - 1, v_v2.0 + 1)) :|: TRUE eval_speedpldi2_bb4_in(v_m, v_n, v_v1.0, v_v2.0) -> Com_1(eval_speedpldi2_stop(v_m, v_n, v_v1.0, v_v2.0)) :|: TRUE The start-symbols are:[eval_speedpldi2_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 20*Ar_0 + 12) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_0, 0)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) (Comp: ?, Cost: 1) evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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) evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_0, 0)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) (Comp: ?, Cost: 1) evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalspeedpldi2start) = 2 Pol(evalspeedpldi2bb0in) = 2 Pol(evalspeedpldi2bb1in) = 2 Pol(evalspeedpldi2bb4in) = 1 Pol(evalspeedpldi2bb2in) = 2 Pol(evalspeedpldi2bb3in) = 2 Pol(evalspeedpldi2stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2stop(Ar_0, Ar_1, Ar_2, Ar_3)) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_0, 0)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: 2, Cost: 1) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) (Comp: 2, Cost: 1) evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalspeedpldi2bb1in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalspeedpldi2bb2in: X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalspeedpldi2bb3in: X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 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) -> Com_1(evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_3 + 1 ] (Comp: 2, Cost: 1) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ] (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_0, 0)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalspeedpldi2bb3in) = 5*V_3 + 2*V_4 - 1 Pol(evalspeedpldi2bb1in) = 5*V_3 + 2*V_4 + 1 Pol(evalspeedpldi2bb2in) = 5*V_3 + 2*V_4 and size complexities S("evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_0, 0)) [ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_0, 0)) [ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_0, 0)) [ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-2) = Ar_0 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_0, 0)) [ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-3) = 0 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-0) = Ar_0 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-1) = Ar_1 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-2) = Ar_2 S("evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-3) = Ar_3 S("evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 ]", 0-0) = Ar_0 S("evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 ]", 0-1) = Ar_1 S("evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 ]", 0-2) = Ar_0 S("evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 ]", 0-3) = Ar_1 S("evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 ]", 0-0) = Ar_0 S("evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 ]", 0-1) = Ar_1 S("evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 ]", 0-2) = 0 S("evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 ]", 0-3) = Ar_1 S("evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-2) = Ar_0 S("evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-3) = Ar_1 S("evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-0) = Ar_0 S("evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-1) = Ar_1 S("evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-2) = Ar_0 S("evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-3) = 0 S("evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = Ar_0 S("evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = Ar_1 S("evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_1 + Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_3 + 1 ] evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_1 ] evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ] weakly and the transitions evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_3 + 1 ] evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_1 ] evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 5*Ar_0 + 1, Cost: 1) evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 5*Ar_0 + 1, Cost: 1) evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_1 ] (Comp: 5*Ar_0 + 1, Cost: 1) evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_3 + 1 ] (Comp: 2, Cost: 1) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 ] (Comp: 5*Ar_0 + 1, Cost: 1) evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ] (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb1in(Ar_0, Ar_1, Ar_0, 0)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalspeedpldi2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 20*Ar_0 + 12 Time: 0.212 sec (SMT: 0.173 sec) ---------------------------------------- (2) BOUNDS(1, n^1)