5.42/2.43 WORST_CASE(Omega(n^1), O(n^1)) 5.42/2.44 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 5.42/2.44 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.42/2.44 5.42/2.44 5.42/2.44 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 5.42/2.44 5.42/2.44 (0) CpxIntTrs 5.42/2.44 (1) Koat Proof [FINISHED, 412 ms] 5.42/2.44 (2) BOUNDS(1, n^1) 5.42/2.44 (3) Loat Proof [FINISHED, 696 ms] 5.42/2.44 (4) BOUNDS(n^1, INF) 5.42/2.44 5.42/2.44 5.42/2.44 ---------------------------------------- 5.42/2.44 5.42/2.44 (0) 5.42/2.44 Obligation: 5.42/2.44 Complexity Int TRS consisting of the following rules: 5.42/2.44 eval_speedDis1_start(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_bb0_in(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE 5.42/2.44 eval_speedDis1_bb0_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_0(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE 5.42/2.44 eval_speedDis1_0(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_1(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE 5.42/2.44 eval_speedDis1_1(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_2(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE 5.42/2.44 eval_speedDis1_2(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_3(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE 5.42/2.44 eval_speedDis1_3(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_4(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE 5.42/2.44 eval_speedDis1_4(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_5(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE 5.42/2.44 eval_speedDis1_5(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_6(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE 5.42/2.44 eval_speedDis1_6(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_bb1_in(v_x, v_y, v_m, v_n, v_x, v_y)) :|: TRUE 5.42/2.44 eval_speedDis1_bb1_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_bb2_in(v__0, v__01, v_m, v_n, v_x, v_y)) :|: v__0 < v_n 5.42/2.44 eval_speedDis1_bb1_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_bb3_in(v__0, v__01, v_m, v_n, v_x, v_y)) :|: v__0 >= v_n 5.42/2.44 eval_speedDis1_bb2_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_bb1_in(v__0, v__01 + 1, v_m, v_n, v_x, v_y)) :|: v__01 < v_m 5.42/2.44 eval_speedDis1_bb2_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_bb1_in(v__0 + 1, v__01 + 1, v_m, v_n, v_x, v_y)) :|: v__01 < v_m && v__01 >= v_m 5.42/2.44 eval_speedDis1_bb2_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_bb1_in(v__0, v__01, v_m, v_n, v_x, v_y)) :|: v__01 >= v_m && v__01 < v_m 5.42/2.44 eval_speedDis1_bb2_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_bb1_in(v__0 + 1, v__01, v_m, v_n, v_x, v_y)) :|: v__01 >= v_m 5.42/2.44 eval_speedDis1_bb3_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_speedDis1_stop(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE 5.42/2.44 5.42/2.44 The start-symbols are:[eval_speedDis1_start_6] 5.42/2.44 5.42/2.44 5.42/2.44 ---------------------------------------- 5.42/2.44 5.42/2.44 (1) Koat Proof (FINISHED) 5.42/2.44 YES(?, 2*ar_1 + 2*ar_4 + 2*ar_3 + 2*ar_5 + 14) 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 Initial complexity problem: 5.42/2.44 5.42/2.44 1: T: 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 /\ ar_2 >= ar_5 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 /\ ar_5 >= ar_2 + 1 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 5.42/2.44 5.42/2.44 start location: koat_start 5.42/2.44 5.42/2.44 leaf cost: 0 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 Testing for reachability in the complexity graph removes the following transitions from problem 1: 5.42/2.44 5.42/2.44 evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 /\ ar_2 >= ar_5 ] 5.42/2.44 5.42/2.44 evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 /\ ar_5 >= ar_2 + 1 ] 5.42/2.44 5.42/2.44 We thus obtain the following problem: 5.42/2.44 5.42/2.44 2: T: 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 5.42/2.44 5.42/2.44 start location: koat_start 5.42/2.44 5.42/2.44 leaf cost: 0 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 Repeatedly propagating knowledge in problem 2 produces the following problem: 5.42/2.44 5.42/2.44 3: T: 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 5.42/2.44 5.42/2.44 start location: koat_start 5.42/2.44 5.42/2.44 leaf cost: 0 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 A polynomial rank function with 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb3in) = 1 5.42/2.44 5.42/2.44 Pol(evalspeedDis1stop) = 0 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb2in) = 2 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb1in) = 2 5.42/2.44 5.42/2.44 Pol(evalspeedDis16) = 2 5.42/2.44 5.42/2.44 Pol(evalspeedDis15) = 2 5.42/2.44 5.42/2.44 Pol(evalspeedDis14) = 2 5.42/2.44 5.42/2.44 Pol(evalspeedDis13) = 2 5.42/2.44 5.42/2.44 Pol(evalspeedDis12) = 2 5.42/2.44 5.42/2.44 Pol(evalspeedDis11) = 2 5.42/2.44 5.42/2.44 Pol(evalspeedDis10) = 2 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb0in) = 2 5.42/2.44 5.42/2.44 Pol(evalspeedDis1start) = 2 5.42/2.44 5.42/2.44 Pol(koat_start) = 2 5.42/2.44 5.42/2.44 orients all transitions weakly and the transitions 5.42/2.44 5.42/2.44 evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] 5.42/2.44 5.42/2.44 strictly and produces the following problem: 5.42/2.44 5.42/2.44 4: T: 5.42/2.44 5.42/2.44 (Comp: 2, Cost: 1) evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] 5.42/2.44 5.42/2.44 (Comp: 2, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 5.42/2.44 5.42/2.44 start location: koat_start 5.42/2.44 5.42/2.44 leaf cost: 0 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 A polynomial rank function with 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb3in) = -V_3 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis1stop) = -V_3 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb2in) = -V_3 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb1in) = -V_3 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis16) = -V_4 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis15) = -V_4 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis14) = -V_4 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis13) = -V_4 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis12) = -V_4 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis11) = -V_4 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis10) = -V_4 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb0in) = -V_4 + V_6 5.42/2.44 5.42/2.44 Pol(evalspeedDis1start) = -V_4 + V_6 5.42/2.44 5.42/2.44 Pol(koat_start) = -V_4 + V_6 5.42/2.44 5.42/2.44 orients all transitions weakly and the transition 5.42/2.44 5.42/2.44 evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] 5.42/2.44 5.42/2.44 strictly and produces the following problem: 5.42/2.44 5.42/2.44 5: T: 5.42/2.44 5.42/2.44 (Comp: 2, Cost: 1) evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] 5.42/2.44 5.42/2.44 (Comp: ar_3 + ar_5, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] 5.42/2.44 5.42/2.44 (Comp: 2, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 5.42/2.44 5.42/2.44 start location: koat_start 5.42/2.44 5.42/2.44 leaf cost: 0 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 Applied AI with 'oct' on problem 5 to obtain the following invariants: 5.42/2.44 5.42/2.44 For symbol evalspeedDis1bb1in: X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 5.42/2.44 5.42/2.44 For symbol evalspeedDis1bb2in: -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 5.42/2.44 5.42/2.44 For symbol evalspeedDis1bb3in: X_1 - X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 This yielded the following problem: 5.42/2.44 5.42/2.44 6: T: 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ] 5.42/2.44 5.42/2.44 (Comp: 2, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ] 5.42/2.44 5.42/2.44 (Comp: ar_3 + ar_5, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ] 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ] 5.42/2.44 5.42/2.44 (Comp: 2, Cost: 1) evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ] 5.42/2.44 5.42/2.44 start location: koat_start 5.42/2.44 5.42/2.44 leaf cost: 0 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 A polynomial rank function with 5.42/2.44 5.42/2.44 Pol(koat_start) = -V_2 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis1start) = -V_2 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb0in) = -V_2 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis10) = -V_2 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis11) = -V_2 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis12) = -V_2 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis13) = -V_2 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis14) = -V_2 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis15) = -V_2 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis16) = -V_2 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb1in) = -V_1 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb2in) = -V_1 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis1bb3in) = -V_1 + V_5 5.42/2.44 5.42/2.44 Pol(evalspeedDis1stop) = -V_1 + V_5 5.42/2.44 5.42/2.44 orients all transitions weakly and the transition 5.42/2.44 5.42/2.44 evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ] 5.42/2.44 5.42/2.44 strictly and produces the following problem: 5.42/2.44 5.42/2.44 7: T: 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: ?, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ] 5.42/2.44 5.42/2.44 (Comp: 2, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ] 5.42/2.44 5.42/2.44 (Comp: ar_3 + ar_5, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ] 5.42/2.44 5.42/2.44 (Comp: ar_1 + ar_4, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ] 5.42/2.44 5.42/2.44 (Comp: 2, Cost: 1) evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ] 5.42/2.44 5.42/2.44 start location: koat_start 5.42/2.44 5.42/2.44 leaf cost: 0 5.42/2.44 5.42/2.44 5.42/2.44 5.42/2.44 Repeatedly propagating knowledge in problem 7 produces the following problem: 5.42/2.44 5.42/2.44 8: T: 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.42/2.44 5.42/2.44 (Comp: 1, Cost: 1) evalspeedDis13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.50/2.44 5.50/2.44 (Comp: 1, Cost: 1) evalspeedDis14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.50/2.44 5.50/2.44 (Comp: 1, Cost: 1) evalspeedDis15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 5.50/2.44 5.50/2.44 (Comp: 1, Cost: 1) evalspeedDis16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 5.50/2.44 5.50/2.44 (Comp: ar_1 + ar_4 + ar_3 + ar_5 + 1, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ] 5.50/2.44 5.50/2.44 (Comp: 2, Cost: 1) evalspeedDis1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ] 5.50/2.44 5.50/2.44 (Comp: ar_3 + ar_5, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ] 5.50/2.44 5.50/2.44 (Comp: ar_1 + ar_4, Cost: 1) evalspeedDis1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ] 5.50/2.44 5.50/2.44 (Comp: 2, Cost: 1) evalspeedDis1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedDis1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ] 5.50/2.44 5.50/2.44 start location: koat_start 5.50/2.44 5.50/2.44 leaf cost: 0 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Complexity upper bound 2*ar_1 + 2*ar_4 + 2*ar_3 + 2*ar_5 + 14 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Time: 0.399 sec (SMT: 0.293 sec) 5.50/2.44 5.50/2.44 5.50/2.44 ---------------------------------------- 5.50/2.44 5.50/2.44 (2) 5.50/2.44 BOUNDS(1, n^1) 5.50/2.44 5.50/2.44 ---------------------------------------- 5.50/2.44 5.50/2.44 (3) Loat Proof (FINISHED) 5.50/2.44 5.50/2.44 5.50/2.44 ### Pre-processing the ITS problem ### 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Initial linear ITS problem 5.50/2.44 5.50/2.44 Start location: evalspeedDis1start 5.50/2.44 5.50/2.44 0: evalspeedDis1start -> evalspeedDis1bb0in : [], cost: 1 5.50/2.44 5.50/2.44 1: evalspeedDis1bb0in -> evalspeedDis10 : [], cost: 1 5.50/2.44 5.50/2.44 2: evalspeedDis10 -> evalspeedDis11 : [], cost: 1 5.50/2.44 5.50/2.44 3: evalspeedDis11 -> evalspeedDis12 : [], cost: 1 5.50/2.44 5.50/2.44 4: evalspeedDis12 -> evalspeedDis13 : [], cost: 1 5.50/2.44 5.50/2.44 5: evalspeedDis13 -> evalspeedDis14 : [], cost: 1 5.50/2.44 5.50/2.44 6: evalspeedDis14 -> evalspeedDis15 : [], cost: 1 5.50/2.44 5.50/2.44 7: evalspeedDis15 -> evalspeedDis16 : [], cost: 1 5.50/2.44 5.50/2.44 8: evalspeedDis16 -> evalspeedDis1bb1in : A'=B, C'=D, [], cost: 1 5.50/2.44 5.50/2.44 9: evalspeedDis1bb1in -> evalspeedDis1bb2in : [ E>=1+A ], cost: 1 5.50/2.44 5.50/2.44 10: evalspeedDis1bb1in -> evalspeedDis1bb3in : [ A>=E ], cost: 1 5.50/2.44 5.50/2.44 11: evalspeedDis1bb2in -> evalspeedDis1bb1in : C'=1+C, [ F>=1+C ], cost: 1 5.50/2.44 5.50/2.44 12: evalspeedDis1bb2in -> evalspeedDis1bb1in : A'=1+A, C'=1+C, [ F>=1+C && C>=F ], cost: 1 5.50/2.44 5.50/2.44 13: evalspeedDis1bb2in -> evalspeedDis1bb1in : [ C>=F && F>=1+C ], cost: 1 5.50/2.44 5.50/2.44 14: evalspeedDis1bb2in -> evalspeedDis1bb1in : A'=1+A, [ C>=F ], cost: 1 5.50/2.44 5.50/2.44 15: evalspeedDis1bb3in -> evalspeedDis1stop : [], cost: 1 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Removed unreachable and leaf rules: 5.50/2.44 5.50/2.44 Start location: evalspeedDis1start 5.50/2.44 5.50/2.44 0: evalspeedDis1start -> evalspeedDis1bb0in : [], cost: 1 5.50/2.44 5.50/2.44 1: evalspeedDis1bb0in -> evalspeedDis10 : [], cost: 1 5.50/2.44 5.50/2.44 2: evalspeedDis10 -> evalspeedDis11 : [], cost: 1 5.50/2.44 5.50/2.44 3: evalspeedDis11 -> evalspeedDis12 : [], cost: 1 5.50/2.44 5.50/2.44 4: evalspeedDis12 -> evalspeedDis13 : [], cost: 1 5.50/2.44 5.50/2.44 5: evalspeedDis13 -> evalspeedDis14 : [], cost: 1 5.50/2.44 5.50/2.44 6: evalspeedDis14 -> evalspeedDis15 : [], cost: 1 5.50/2.44 5.50/2.44 7: evalspeedDis15 -> evalspeedDis16 : [], cost: 1 5.50/2.44 5.50/2.44 8: evalspeedDis16 -> evalspeedDis1bb1in : A'=B, C'=D, [], cost: 1 5.50/2.44 5.50/2.44 9: evalspeedDis1bb1in -> evalspeedDis1bb2in : [ E>=1+A ], cost: 1 5.50/2.44 5.50/2.44 11: evalspeedDis1bb2in -> evalspeedDis1bb1in : C'=1+C, [ F>=1+C ], cost: 1 5.50/2.44 5.50/2.44 12: evalspeedDis1bb2in -> evalspeedDis1bb1in : A'=1+A, C'=1+C, [ F>=1+C && C>=F ], cost: 1 5.50/2.44 5.50/2.44 13: evalspeedDis1bb2in -> evalspeedDis1bb1in : [ C>=F && F>=1+C ], cost: 1 5.50/2.44 5.50/2.44 14: evalspeedDis1bb2in -> evalspeedDis1bb1in : A'=1+A, [ C>=F ], cost: 1 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Removed rules with unsatisfiable guard: 5.50/2.44 5.50/2.44 Start location: evalspeedDis1start 5.50/2.44 5.50/2.44 0: evalspeedDis1start -> evalspeedDis1bb0in : [], cost: 1 5.50/2.44 5.50/2.44 1: evalspeedDis1bb0in -> evalspeedDis10 : [], cost: 1 5.50/2.44 5.50/2.44 2: evalspeedDis10 -> evalspeedDis11 : [], cost: 1 5.50/2.44 5.50/2.44 3: evalspeedDis11 -> evalspeedDis12 : [], cost: 1 5.50/2.44 5.50/2.44 4: evalspeedDis12 -> evalspeedDis13 : [], cost: 1 5.50/2.44 5.50/2.44 5: evalspeedDis13 -> evalspeedDis14 : [], cost: 1 5.50/2.44 5.50/2.44 6: evalspeedDis14 -> evalspeedDis15 : [], cost: 1 5.50/2.44 5.50/2.44 7: evalspeedDis15 -> evalspeedDis16 : [], cost: 1 5.50/2.44 5.50/2.44 8: evalspeedDis16 -> evalspeedDis1bb1in : A'=B, C'=D, [], cost: 1 5.50/2.44 5.50/2.44 9: evalspeedDis1bb1in -> evalspeedDis1bb2in : [ E>=1+A ], cost: 1 5.50/2.44 5.50/2.44 11: evalspeedDis1bb2in -> evalspeedDis1bb1in : C'=1+C, [ F>=1+C ], cost: 1 5.50/2.44 5.50/2.44 14: evalspeedDis1bb2in -> evalspeedDis1bb1in : A'=1+A, [ C>=F ], cost: 1 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 ### Simplification by acceleration and chaining ### 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Eliminated locations (on linear paths): 5.50/2.44 5.50/2.44 Start location: evalspeedDis1start 5.50/2.44 5.50/2.44 23: evalspeedDis1start -> evalspeedDis1bb1in : A'=B, C'=D, [], cost: 9 5.50/2.44 5.50/2.44 9: evalspeedDis1bb1in -> evalspeedDis1bb2in : [ E>=1+A ], cost: 1 5.50/2.44 5.50/2.44 11: evalspeedDis1bb2in -> evalspeedDis1bb1in : C'=1+C, [ F>=1+C ], cost: 1 5.50/2.44 5.50/2.44 14: evalspeedDis1bb2in -> evalspeedDis1bb1in : A'=1+A, [ C>=F ], cost: 1 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Eliminated locations (on tree-shaped paths): 5.50/2.44 5.50/2.44 Start location: evalspeedDis1start 5.50/2.44 5.50/2.44 23: evalspeedDis1start -> evalspeedDis1bb1in : A'=B, C'=D, [], cost: 9 5.50/2.44 5.50/2.44 24: evalspeedDis1bb1in -> evalspeedDis1bb1in : C'=1+C, [ E>=1+A && F>=1+C ], cost: 2 5.50/2.44 5.50/2.44 25: evalspeedDis1bb1in -> evalspeedDis1bb1in : A'=1+A, [ E>=1+A && C>=F ], cost: 2 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Accelerating simple loops of location 9. 5.50/2.44 5.50/2.44 Accelerating the following rules: 5.50/2.44 5.50/2.44 24: evalspeedDis1bb1in -> evalspeedDis1bb1in : C'=1+C, [ E>=1+A && F>=1+C ], cost: 2 5.50/2.44 5.50/2.44 25: evalspeedDis1bb1in -> evalspeedDis1bb1in : A'=1+A, [ E>=1+A && C>=F ], cost: 2 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Accelerated rule 24 with metering function F-C, yielding the new rule 26. 5.50/2.44 5.50/2.44 Accelerated rule 25 with metering function -A+E, yielding the new rule 27. 5.50/2.44 5.50/2.44 Removing the simple loops: 24 25. 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Accelerated all simple loops using metering functions (where possible): 5.50/2.44 5.50/2.44 Start location: evalspeedDis1start 5.50/2.44 5.50/2.44 23: evalspeedDis1start -> evalspeedDis1bb1in : A'=B, C'=D, [], cost: 9 5.50/2.44 5.50/2.44 26: evalspeedDis1bb1in -> evalspeedDis1bb1in : C'=F, [ E>=1+A && F>=1+C ], cost: 2*F-2*C 5.50/2.44 5.50/2.44 27: evalspeedDis1bb1in -> evalspeedDis1bb1in : A'=E, [ E>=1+A && C>=F ], cost: -2*A+2*E 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Chained accelerated rules (with incoming rules): 5.50/2.44 5.50/2.44 Start location: evalspeedDis1start 5.50/2.44 5.50/2.44 23: evalspeedDis1start -> evalspeedDis1bb1in : A'=B, C'=D, [], cost: 9 5.50/2.44 5.50/2.44 28: evalspeedDis1start -> evalspeedDis1bb1in : A'=B, C'=F, [ E>=1+B && F>=1+D ], cost: 9+2*F-2*D 5.50/2.44 5.50/2.44 29: evalspeedDis1start -> evalspeedDis1bb1in : A'=E, C'=D, [ E>=1+B && D>=F ], cost: 9+2*E-2*B 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Removed unreachable locations (and leaf rules with constant cost): 5.50/2.44 5.50/2.44 Start location: evalspeedDis1start 5.50/2.44 5.50/2.44 28: evalspeedDis1start -> evalspeedDis1bb1in : A'=B, C'=F, [ E>=1+B && F>=1+D ], cost: 9+2*F-2*D 5.50/2.44 5.50/2.44 29: evalspeedDis1start -> evalspeedDis1bb1in : A'=E, C'=D, [ E>=1+B && D>=F ], cost: 9+2*E-2*B 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 ### Computing asymptotic complexity ### 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Fully simplified ITS problem 5.50/2.44 5.50/2.44 Start location: evalspeedDis1start 5.50/2.44 5.50/2.44 28: evalspeedDis1start -> evalspeedDis1bb1in : A'=B, C'=F, [ E>=1+B && F>=1+D ], cost: 9+2*F-2*D 5.50/2.44 5.50/2.44 29: evalspeedDis1start -> evalspeedDis1bb1in : A'=E, C'=D, [ E>=1+B && D>=F ], cost: 9+2*E-2*B 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Computing asymptotic complexity for rule 28 5.50/2.44 5.50/2.44 Solved the limit problem by the following transformations: 5.50/2.44 5.50/2.44 Created initial limit problem: 5.50/2.44 5.50/2.44 9+2*F-2*D (+), F-D (+/+!), E-B (+/+!) [not solved] 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 removing all constraints (solved by SMT) 5.50/2.44 5.50/2.44 resulting limit problem: [solved] 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 applying transformation rule (C) using substitution {F==0,D==-n,E==1,B==0} 5.50/2.44 5.50/2.44 resulting limit problem: 5.50/2.44 5.50/2.44 [solved] 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Solution: 5.50/2.44 5.50/2.44 F / 0 5.50/2.44 5.50/2.44 D / -n 5.50/2.44 5.50/2.44 E / 1 5.50/2.44 5.50/2.44 B / 0 5.50/2.44 5.50/2.44 Resulting cost 9+2*n has complexity: Poly(n^1) 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Found new complexity Poly(n^1). 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 Obtained the following overall complexity (w.r.t. the length of the input n): 5.50/2.44 5.50/2.44 Complexity: Poly(n^1) 5.50/2.44 5.50/2.44 Cpx degree: 1 5.50/2.44 5.50/2.44 Solved cost: 9+2*n 5.50/2.44 5.50/2.44 Rule cost: 9+2*F-2*D 5.50/2.44 5.50/2.44 Rule guard: [ E>=1+B && F>=1+D ] 5.50/2.44 5.50/2.44 5.50/2.44 5.50/2.44 WORST_CASE(Omega(n^1),?) 5.50/2.44 5.50/2.44 5.50/2.44 ---------------------------------------- 5.50/2.44 5.50/2.44 (4) 5.50/2.44 BOUNDS(n^1, INF) 5.50/2.46 EOF