5.32/2.58 WORST_CASE(Omega(n^2), O(n^2)) 5.32/2.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 5.32/2.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.32/2.59 5.32/2.59 5.32/2.59 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 5.32/2.59 5.32/2.59 (0) CpxIntTrs 5.32/2.59 (1) Koat Proof [FINISHED, 102 ms] 5.32/2.59 (2) BOUNDS(1, n^2) 5.32/2.59 (3) Loat Proof [FINISHED, 810 ms] 5.32/2.59 (4) BOUNDS(n^2, INF) 5.32/2.59 5.32/2.59 5.32/2.59 ---------------------------------------- 5.32/2.59 5.32/2.59 (0) 5.32/2.59 Obligation: 5.32/2.59 Complexity Int TRS consisting of the following rules: 5.32/2.59 eval_abc_start(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb0_in(v_4, v_i_0, v_j_0, v_n)) :|: TRUE 5.32/2.59 eval_abc_bb0_in(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_0(v_4, v_i_0, v_j_0, v_n)) :|: TRUE 5.32/2.59 eval_abc_0(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_1(v_4, v_i_0, v_j_0, v_n)) :|: TRUE 5.32/2.59 eval_abc_1(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_2(v_4, v_i_0, v_j_0, v_n)) :|: TRUE 5.32/2.59 eval_abc_2(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_3(v_4, v_i_0, v_j_0, v_n)) :|: TRUE 5.32/2.59 eval_abc_3(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_4(v_4, v_i_0, v_j_0, v_n)) :|: TRUE 5.32/2.59 eval_abc_4(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb1_in(v_4, 0, v_j_0, v_n)) :|: TRUE 5.32/2.59 eval_abc_bb1_in(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb2_in(v_4, v_i_0, 0, v_n)) :|: v_i_0 <= v_n - 1 5.32/2.59 eval_abc_bb1_in(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb5_in(v_4, v_i_0, v_j_0, v_n)) :|: v_i_0 > v_n - 1 5.32/2.59 eval_abc_bb2_in(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb3_in(v_4, v_i_0, v_j_0, v_n)) :|: v_j_0 <= v_i_0 5.32/2.59 eval_abc_bb2_in(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb4_in(v_4, v_i_0, v_j_0, v_n)) :|: v_j_0 > v_i_0 5.32/2.59 eval_abc_bb3_in(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb2_in(v_4, v_i_0, v_j_0 + 1, v_n)) :|: TRUE 5.32/2.59 eval_abc_bb4_in(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_10(v_i_0 + 1, v_i_0, v_j_0, v_n)) :|: TRUE 5.32/2.59 eval_abc_10(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_11(v_4, v_i_0, v_j_0, v_n)) :|: TRUE 5.32/2.59 eval_abc_11(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb1_in(v_4, v_4, v_j_0, v_n)) :|: TRUE 5.32/2.59 eval_abc_bb5_in(v_4, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_stop(v_4, v_i_0, v_j_0, v_n)) :|: TRUE 5.32/2.59 5.32/2.59 The start-symbols are:[eval_abc_start_4] 5.32/2.59 5.32/2.59 5.32/2.59 ---------------------------------------- 5.32/2.59 5.32/2.59 (1) Koat Proof (FINISHED) 5.32/2.59 YES(?, 155*ar_1 + 8*ar_1^2 + 158) 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Initial complexity problem: 5.32/2.59 5.32/2.59 1: T: 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 5.32/2.59 5.32/2.59 start location: koat_start 5.32/2.59 5.32/2.59 leaf cost: 0 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Repeatedly propagating knowledge in problem 1 produces the following problem: 5.32/2.59 5.32/2.59 2: T: 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 5.32/2.59 5.32/2.59 start location: koat_start 5.32/2.59 5.32/2.59 leaf cost: 0 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 A polynomial rank function with 5.32/2.59 5.32/2.59 Pol(evalabcstart) = 2 5.32/2.59 5.32/2.59 Pol(evalabcbb0in) = 2 5.32/2.59 5.32/2.59 Pol(evalabc0) = 2 5.32/2.59 5.32/2.59 Pol(evalabc1) = 2 5.32/2.59 5.32/2.59 Pol(evalabc2) = 2 5.32/2.59 5.32/2.59 Pol(evalabc3) = 2 5.32/2.59 5.32/2.59 Pol(evalabc4) = 2 5.32/2.59 5.32/2.59 Pol(evalabcbb1in) = 2 5.32/2.59 5.32/2.59 Pol(evalabcbb2in) = 2 5.32/2.59 5.32/2.59 Pol(evalabcbb5in) = 1 5.32/2.59 5.32/2.59 Pol(evalabcbb3in) = 2 5.32/2.59 5.32/2.59 Pol(evalabcbb4in) = 2 5.32/2.59 5.32/2.59 Pol(evalabc10) = 2 5.32/2.59 5.32/2.59 Pol(evalabc11) = 2 5.32/2.59 5.32/2.59 Pol(evalabcstop) = 0 5.32/2.59 5.32/2.59 Pol(koat_start) = 2 5.32/2.59 5.32/2.59 orients all transitions weakly and the transitions 5.32/2.59 5.32/2.59 evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 5.32/2.59 5.32/2.59 strictly and produces the following problem: 5.32/2.59 5.32/2.59 3: T: 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: 2, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 5.32/2.59 5.32/2.59 start location: koat_start 5.32/2.59 5.32/2.59 leaf cost: 0 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 A polynomial rank function with 5.32/2.59 5.32/2.59 Pol(evalabcstart) = V_2 + 1 5.32/2.59 5.32/2.59 Pol(evalabcbb0in) = V_2 + 1 5.32/2.59 5.32/2.59 Pol(evalabc0) = V_2 + 1 5.32/2.59 5.32/2.59 Pol(evalabc1) = V_2 + 1 5.32/2.59 5.32/2.59 Pol(evalabc2) = V_2 + 1 5.32/2.59 5.32/2.59 Pol(evalabc3) = V_2 + 1 5.32/2.59 5.32/2.59 Pol(evalabc4) = V_2 + 1 5.32/2.59 5.32/2.59 Pol(evalabcbb1in) = -V_1 + V_2 + 1 5.32/2.59 5.32/2.59 Pol(evalabcbb2in) = -V_1 + V_2 5.32/2.59 5.32/2.59 Pol(evalabcbb5in) = -V_1 + V_2 5.32/2.59 5.32/2.59 Pol(evalabcbb3in) = -V_1 + V_2 5.32/2.59 5.32/2.59 Pol(evalabcbb4in) = -V_1 + V_2 5.32/2.59 5.32/2.59 Pol(evalabc10) = V_2 - V_4 + 1 5.32/2.59 5.32/2.59 Pol(evalabc11) = V_2 - V_4 + 1 5.32/2.59 5.32/2.59 Pol(evalabcstop) = -V_1 + V_2 5.32/2.59 5.32/2.59 Pol(koat_start) = V_2 + 1 5.32/2.59 5.32/2.59 orients all transitions weakly and the transition 5.32/2.59 5.32/2.59 evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 strictly and produces the following problem: 5.32/2.59 5.32/2.59 4: T: 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ar_1 + 1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: 2, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 5.32/2.59 5.32/2.59 start location: koat_start 5.32/2.59 5.32/2.59 leaf cost: 0 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 A polynomial rank function with 5.32/2.59 5.32/2.59 Pol(evalabcbb4in) = 3 5.32/2.59 5.32/2.59 Pol(evalabc10) = 2 5.32/2.59 5.32/2.59 Pol(evalabcbb3in) = 4 5.32/2.59 5.32/2.59 Pol(evalabcbb2in) = 4 5.32/2.59 5.32/2.59 Pol(evalabc11) = 1 5.32/2.59 5.32/2.59 Pol(evalabcbb1in) = 0 5.32/2.59 5.32/2.59 and size complexities 5.32/2.59 5.32/2.59 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 5.32/2.59 5.32/2.59 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 5.32/2.59 5.32/2.59 S("evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = ? 5.32/2.59 5.32/2.59 S("evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = ? 5.32/2.59 5.32/2.59 S("evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 5.32/2.59 5.32/2.59 S("evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 5.32/2.59 5.32/2.59 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = ? 5.32/2.59 5.32/2.59 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = ? 5.32/2.59 5.32/2.59 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = ? 5.32/2.59 5.32/2.59 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = ? 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-0) = ? 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-3) = ? 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-0) = ? 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-3) = ? 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = ? 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = ? 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ? 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-2) = 0 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-3) = ? 5.32/2.59 5.32/2.59 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-0) = 0 5.32/2.59 5.32/2.59 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 orients the transitions 5.32/2.59 5.32/2.59 evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1)) 5.32/2.59 5.32/2.59 evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.32/2.59 5.32/2.59 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 5.32/2.59 5.32/2.59 evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 weakly and the transitions 5.32/2.59 5.32/2.59 evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1)) 5.32/2.59 5.32/2.59 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 strictly and produces the following problem: 5.32/2.59 5.32/2.59 5: T: 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ar_1 + 1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: 2, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1)) 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 5.32/2.59 5.32/2.59 start location: koat_start 5.32/2.59 5.32/2.59 leaf cost: 0 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 A polynomial rank function with 5.32/2.59 5.32/2.59 Pol(evalabcbb3in) = V_1 - V_3 5.32/2.59 5.32/2.59 Pol(evalabcbb2in) = V_1 - V_3 + 1 5.32/2.59 5.32/2.59 and size complexities 5.32/2.59 5.32/2.59 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 4*ar_1 + 1024 5.32/2.59 5.32/2.59 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = 4*ar_1 + 4*ar_3 + 4096 5.32/2.59 5.32/2.59 S("evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = 4*ar_1 + 64 5.32/2.59 5.32/2.59 S("evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = 4*ar_1 + 256 5.32/2.59 5.32/2.59 S("evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3))", 0-0) = 4*ar_1 + 1024 5.32/2.59 5.32/2.59 S("evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3))", 0-3) = 4*ar_1 + 64 5.32/2.59 5.32/2.59 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = 4*ar_1 + 256 5.32/2.59 5.32/2.59 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = 4*ar_1 + 64 5.32/2.59 5.32/2.59 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = 4*ar_1 + 64 5.32/2.59 5.32/2.59 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = 4*ar_1 + 4*ar_3 + 4096 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-0) = 4*ar_1 + 64 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-3) = 4*ar_1 + 4*ar_3 + 16384 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-0) = 4*ar_1 + 64 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]", 0-3) = 4*ar_1 + 4*ar_3 + 4096 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = 4*ar_1 + 256 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ? 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = 4*ar_1 + 4*ar_3 + 1024 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-0) = 4*ar_1 + 64 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-2) = 0 5.32/2.59 5.32/2.59 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-3) = 4*ar_1 + 4*ar_3 + 1024 5.32/2.59 5.32/2.59 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-0) = 0 5.32/2.59 5.32/2.59 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 5.32/2.59 5.32/2.59 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.32/2.59 5.32/2.59 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.32/2.59 5.32/2.59 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.32/2.59 5.32/2.59 orients the transitions 5.32/2.59 5.32/2.59 evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.32/2.59 5.32/2.59 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 5.32/2.59 5.32/2.59 weakly and the transition 5.32/2.59 5.32/2.59 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 5.32/2.59 5.32/2.59 strictly and produces the following problem: 5.32/2.59 5.32/2.59 6: T: 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ar_1 + 1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: 2, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 5.32/2.59 5.32/2.59 (Comp: 4*ar_1^2 + 69*ar_1 + 65, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1)) 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 5.32/2.59 5.32/2.59 start location: koat_start 5.32/2.59 5.32/2.59 leaf cost: 0 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Repeatedly propagating knowledge in problem 6 produces the following problem: 5.32/2.59 5.32/2.59 7: T: 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: ar_1 + 1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: 2, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 5.32/2.59 5.32/2.59 (Comp: 4*ar_1^2 + 69*ar_1 + 65, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 5.32/2.59 5.32/2.59 (Comp: 4*ar_1^2 + 69*ar_1 + 65, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_0 + 1)) 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabc10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc11(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 4*ar_1 + 4, Cost: 1) evalabc11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.32/2.59 5.32/2.59 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 5.32/2.59 5.32/2.59 start location: koat_start 5.32/2.59 5.32/2.59 leaf cost: 0 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Complexity upper bound 155*ar_1 + 8*ar_1^2 + 158 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Time: 0.171 sec (SMT: 0.130 sec) 5.32/2.59 5.32/2.59 5.32/2.59 ---------------------------------------- 5.32/2.59 5.32/2.59 (2) 5.32/2.59 BOUNDS(1, n^2) 5.32/2.59 5.32/2.59 ---------------------------------------- 5.32/2.59 5.32/2.59 (3) Loat Proof (FINISHED) 5.32/2.59 5.32/2.59 5.32/2.59 ### Pre-processing the ITS problem ### 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Initial linear ITS problem 5.32/2.59 5.32/2.59 Start location: evalabcstart 5.32/2.59 5.32/2.59 0: evalabcstart -> evalabcbb0in : [], cost: 1 5.32/2.59 5.32/2.59 1: evalabcbb0in -> evalabc0 : [], cost: 1 5.32/2.59 5.32/2.59 2: evalabc0 -> evalabc1 : [], cost: 1 5.32/2.59 5.32/2.59 3: evalabc1 -> evalabc2 : [], cost: 1 5.32/2.59 5.32/2.59 4: evalabc2 -> evalabc3 : [], cost: 1 5.32/2.59 5.32/2.59 5: evalabc3 -> evalabc4 : [], cost: 1 5.32/2.59 5.32/2.59 6: evalabc4 -> evalabcbb1in : A'=0, [], cost: 1 5.32/2.59 5.32/2.59 7: evalabcbb1in -> evalabcbb2in : C'=0, [ B>=1+A ], cost: 1 5.32/2.59 5.32/2.59 8: evalabcbb1in -> evalabcbb5in : [ A>=B ], cost: 1 5.32/2.59 5.32/2.59 9: evalabcbb2in -> evalabcbb3in : [ A>=C ], cost: 1 5.32/2.59 5.32/2.59 10: evalabcbb2in -> evalabcbb4in : [ C>=1+A ], cost: 1 5.32/2.59 5.32/2.59 11: evalabcbb3in -> evalabcbb2in : C'=1+C, [], cost: 1 5.32/2.59 5.32/2.59 12: evalabcbb4in -> evalabc10 : D'=1+A, [], cost: 1 5.32/2.59 5.32/2.59 13: evalabc10 -> evalabc11 : [], cost: 1 5.32/2.59 5.32/2.59 14: evalabc11 -> evalabcbb1in : A'=D, [], cost: 1 5.32/2.59 5.32/2.59 15: evalabcbb5in -> evalabcstop : [], cost: 1 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Removed unreachable and leaf rules: 5.32/2.59 5.32/2.59 Start location: evalabcstart 5.32/2.59 5.32/2.59 0: evalabcstart -> evalabcbb0in : [], cost: 1 5.32/2.59 5.32/2.59 1: evalabcbb0in -> evalabc0 : [], cost: 1 5.32/2.59 5.32/2.59 2: evalabc0 -> evalabc1 : [], cost: 1 5.32/2.59 5.32/2.59 3: evalabc1 -> evalabc2 : [], cost: 1 5.32/2.59 5.32/2.59 4: evalabc2 -> evalabc3 : [], cost: 1 5.32/2.59 5.32/2.59 5: evalabc3 -> evalabc4 : [], cost: 1 5.32/2.59 5.32/2.59 6: evalabc4 -> evalabcbb1in : A'=0, [], cost: 1 5.32/2.59 5.32/2.59 7: evalabcbb1in -> evalabcbb2in : C'=0, [ B>=1+A ], cost: 1 5.32/2.59 5.32/2.59 9: evalabcbb2in -> evalabcbb3in : [ A>=C ], cost: 1 5.32/2.59 5.32/2.59 10: evalabcbb2in -> evalabcbb4in : [ C>=1+A ], cost: 1 5.32/2.59 5.32/2.59 11: evalabcbb3in -> evalabcbb2in : C'=1+C, [], cost: 1 5.32/2.59 5.32/2.59 12: evalabcbb4in -> evalabc10 : D'=1+A, [], cost: 1 5.32/2.59 5.32/2.59 13: evalabc10 -> evalabc11 : [], cost: 1 5.32/2.59 5.32/2.59 14: evalabc11 -> evalabcbb1in : A'=D, [], cost: 1 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 ### Simplification by acceleration and chaining ### 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Eliminated locations (on linear paths): 5.32/2.59 5.32/2.59 Start location: evalabcstart 5.32/2.59 5.32/2.59 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 5.32/2.59 5.32/2.59 7: evalabcbb1in -> evalabcbb2in : C'=0, [ B>=1+A ], cost: 1 5.32/2.59 5.32/2.59 22: evalabcbb2in -> evalabcbb2in : C'=1+C, [ A>=C ], cost: 2 5.32/2.59 5.32/2.59 25: evalabcbb2in -> evalabcbb1in : A'=1+A, D'=1+A, [ C>=1+A ], cost: 4 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Accelerating simple loops of location 8. 5.32/2.59 5.32/2.59 Accelerating the following rules: 5.32/2.59 5.32/2.59 22: evalabcbb2in -> evalabcbb2in : C'=1+C, [ A>=C ], cost: 2 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Accelerated rule 22 with metering function 1-C+A, yielding the new rule 26. 5.32/2.59 5.32/2.59 Removing the simple loops: 22. 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Accelerated all simple loops using metering functions (where possible): 5.32/2.59 5.32/2.59 Start location: evalabcstart 5.32/2.59 5.32/2.59 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 5.32/2.59 5.32/2.59 7: evalabcbb1in -> evalabcbb2in : C'=0, [ B>=1+A ], cost: 1 5.32/2.59 5.32/2.59 25: evalabcbb2in -> evalabcbb1in : A'=1+A, D'=1+A, [ C>=1+A ], cost: 4 5.32/2.59 5.32/2.59 26: evalabcbb2in -> evalabcbb2in : C'=1+A, [ A>=C ], cost: 2-2*C+2*A 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Chained accelerated rules (with incoming rules): 5.32/2.59 5.32/2.59 Start location: evalabcstart 5.32/2.59 5.32/2.59 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 5.32/2.59 5.32/2.59 7: evalabcbb1in -> evalabcbb2in : C'=0, [ B>=1+A ], cost: 1 5.32/2.59 5.32/2.59 27: evalabcbb1in -> evalabcbb2in : C'=1+A, [ B>=1+A && A>=0 ], cost: 3+2*A 5.32/2.59 5.32/2.59 25: evalabcbb2in -> evalabcbb1in : A'=1+A, D'=1+A, [ C>=1+A ], cost: 4 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Eliminated locations (on tree-shaped paths): 5.32/2.59 5.32/2.59 Start location: evalabcstart 5.32/2.59 5.32/2.59 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 5.32/2.59 5.32/2.59 28: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=0, D'=1+A, [ B>=1+A && 0>=1+A ], cost: 5 5.32/2.59 5.32/2.59 29: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1+A, D'=1+A, [ B>=1+A && A>=0 ], cost: 7+2*A 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Accelerating simple loops of location 7. 5.32/2.59 5.32/2.59 Accelerating the following rules: 5.32/2.59 5.32/2.59 28: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=0, D'=1+A, [ B>=1+A && 0>=1+A ], cost: 5 5.32/2.59 5.32/2.59 29: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1+A, D'=1+A, [ B>=1+A && A>=0 ], cost: 7+2*A 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Accelerated rule 28 with backward acceleration, yielding the new rule 30. 5.32/2.59 5.32/2.59 Accelerated rule 28 with backward acceleration, yielding the new rule 31. 5.32/2.59 5.32/2.59 Accelerated rule 29 with metering function -A+B, yielding the new rule 32. 5.32/2.59 5.32/2.59 Removing the simple loops: 28 29. 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Accelerated all simple loops using metering functions (where possible): 5.32/2.59 5.32/2.59 Start location: evalabcstart 5.32/2.59 5.32/2.59 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 5.32/2.59 5.32/2.59 30: evalabcbb1in -> evalabcbb1in : A'=B, C'=0, D'=B, [ B>=1+A && 0>=1+A && 0>=B ], cost: -5*A+5*B 5.32/2.59 5.32/2.59 31: evalabcbb1in -> evalabcbb1in : A'=0, C'=0, D'=0, [ B>=1+A && 0>=1+A && B>=0 ], cost: -5*A 5.32/2.59 5.32/2.59 32: evalabcbb1in -> evalabcbb1in : A'=B, C'=B, D'=B, [ B>=1+A && A>=0 ], cost: (A-B)^2-6*A-2*A*(A-B)+6*B 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Chained accelerated rules (with incoming rules): 5.32/2.59 5.32/2.59 Start location: evalabcstart 5.32/2.59 5.32/2.59 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 5.32/2.59 5.32/2.59 33: evalabcstart -> evalabcbb1in : A'=B, C'=B, D'=B, [ B>=1 ], cost: 7+B^2+6*B 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Removed unreachable locations (and leaf rules with constant cost): 5.32/2.59 5.32/2.59 Start location: evalabcstart 5.32/2.59 5.32/2.59 33: evalabcstart -> evalabcbb1in : A'=B, C'=B, D'=B, [ B>=1 ], cost: 7+B^2+6*B 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 ### Computing asymptotic complexity ### 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Fully simplified ITS problem 5.32/2.59 5.32/2.59 Start location: evalabcstart 5.32/2.59 5.32/2.59 33: evalabcstart -> evalabcbb1in : A'=B, C'=B, D'=B, [ B>=1 ], cost: 7+B^2+6*B 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Computing asymptotic complexity for rule 33 5.32/2.59 5.32/2.59 Solved the limit problem by the following transformations: 5.32/2.59 5.32/2.59 Created initial limit problem: 5.32/2.59 5.32/2.59 7+B^2+6*B (+), B (+/+!) [not solved] 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 removing all constraints (solved by SMT) 5.32/2.59 5.32/2.59 resulting limit problem: [solved] 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 applying transformation rule (C) using substitution {B==n} 5.32/2.59 5.32/2.59 resulting limit problem: 5.32/2.59 5.32/2.59 [solved] 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Solution: 5.32/2.59 5.32/2.59 B / n 5.32/2.59 5.32/2.59 Resulting cost 7+n^2+6*n has complexity: Poly(n^2) 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Found new complexity Poly(n^2). 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 Obtained the following overall complexity (w.r.t. the length of the input n): 5.32/2.59 5.32/2.59 Complexity: Poly(n^2) 5.32/2.59 5.32/2.59 Cpx degree: 2 5.32/2.59 5.32/2.59 Solved cost: 7+n^2+6*n 5.32/2.59 5.32/2.59 Rule cost: 7+B^2+6*B 5.32/2.59 5.32/2.59 Rule guard: [ B>=1 ] 5.32/2.59 5.32/2.59 5.32/2.59 5.32/2.59 WORST_CASE(Omega(n^2),?) 5.32/2.59 5.32/2.59 5.32/2.59 ---------------------------------------- 5.32/2.59 5.32/2.59 (4) 5.32/2.59 BOUNDS(n^2, INF) 5.55/2.61 EOF