5.07/2.34 WORST_CASE(Omega(n^2), O(n^2)) 5.07/2.35 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 5.07/2.35 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.07/2.35 5.07/2.35 5.07/2.35 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 5.07/2.35 5.07/2.35 (0) CpxIntTrs 5.07/2.35 (1) Koat Proof [FINISHED, 203 ms] 5.07/2.35 (2) BOUNDS(1, n^2) 5.07/2.35 (3) Loat Proof [FINISHED, 704 ms] 5.07/2.35 (4) BOUNDS(n^2, INF) 5.07/2.35 5.07/2.35 5.07/2.35 ---------------------------------------- 5.07/2.35 5.07/2.35 (0) 5.07/2.35 Obligation: 5.07/2.35 Complexity Int TRS consisting of the following rules: 5.07/2.35 eval_abc_start(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb0_in(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 5.07/2.35 eval_abc_bb0_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_0(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 5.07/2.35 eval_abc_0(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_1(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 5.07/2.35 eval_abc_1(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_2(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 5.07/2.35 eval_abc_2(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_3(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 5.07/2.35 eval_abc_3(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_4(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 5.07/2.35 eval_abc_4(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb1_in(v_3, 1, v_j_0, v_n)) :|: TRUE 5.07/2.35 eval_abc_bb1_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb2_in(v_3, v_i_0, 1, v_n)) :|: v_i_0 <= v_n 5.07/2.35 eval_abc_bb1_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb5_in(v_3, v_i_0, v_j_0, v_n)) :|: v_i_0 > v_n 5.07/2.35 eval_abc_bb2_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb3_in(v_3, v_i_0, v_j_0, v_n)) :|: v_j_0 <= v_n 5.07/2.35 eval_abc_bb2_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb4_in(v_3, v_i_0, v_j_0, v_n)) :|: v_j_0 > v_n 5.07/2.35 eval_abc_bb3_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb2_in(v_3, v_i_0, v_j_0 + 1, v_n)) :|: TRUE 5.07/2.35 eval_abc_bb4_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_8(v_i_0 + 1, v_i_0, v_j_0, v_n)) :|: TRUE 5.07/2.35 eval_abc_8(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_9(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 5.07/2.35 eval_abc_9(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb1_in(v_3, v_3, v_j_0, v_n)) :|: TRUE 5.07/2.35 eval_abc_bb5_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_stop(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 5.07/2.35 5.07/2.35 The start-symbols are:[eval_abc_start_4] 5.07/2.35 5.07/2.35 5.07/2.35 ---------------------------------------- 5.07/2.35 5.07/2.35 (1) Koat Proof (FINISHED) 5.07/2.35 YES(?, 21*ar_1 + 2*ar_1^2 + 11) 5.07/2.35 5.07/2.35 5.07/2.35 5.07/2.35 Initial complexity problem: 5.07/2.35 5.07/2.35 1: T: 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ] 5.07/2.35 5.07/2.35 (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 + 1 ] 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 5.07/2.35 5.07/2.35 (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_1 + 1 ] 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (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 ] 5.07/2.35 5.07/2.35 start location: koat_start 5.07/2.35 5.07/2.35 leaf cost: 0 5.07/2.35 5.07/2.35 5.07/2.35 5.07/2.35 Repeatedly propagating knowledge in problem 1 produces the following problem: 5.07/2.35 5.07/2.35 2: T: 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ] 5.07/2.35 5.07/2.35 (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 + 1 ] 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 5.07/2.35 5.07/2.35 (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_1 + 1 ] 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (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 ] 5.07/2.35 5.07/2.35 start location: koat_start 5.07/2.35 5.07/2.35 leaf cost: 0 5.07/2.35 5.07/2.35 5.07/2.35 5.07/2.35 A polynomial rank function with 5.07/2.35 5.07/2.35 Pol(evalabcstart) = 2 5.07/2.35 5.07/2.35 Pol(evalabcbb0in) = 2 5.07/2.35 5.07/2.35 Pol(evalabc0) = 2 5.07/2.35 5.07/2.35 Pol(evalabc1) = 2 5.07/2.35 5.07/2.35 Pol(evalabc2) = 2 5.07/2.35 5.07/2.35 Pol(evalabc3) = 2 5.07/2.35 5.07/2.35 Pol(evalabc4) = 2 5.07/2.35 5.07/2.35 Pol(evalabcbb1in) = 2 5.07/2.35 5.07/2.35 Pol(evalabcbb2in) = 2 5.07/2.35 5.07/2.35 Pol(evalabcbb5in) = 1 5.07/2.35 5.07/2.35 Pol(evalabcbb3in) = 2 5.07/2.35 5.07/2.35 Pol(evalabcbb4in) = 2 5.07/2.35 5.07/2.35 Pol(evalabc8) = 2 5.07/2.35 5.07/2.35 Pol(evalabc9) = 2 5.07/2.35 5.07/2.35 Pol(evalabcstop) = 0 5.07/2.35 5.07/2.35 Pol(koat_start) = 2 5.07/2.35 5.07/2.35 orients all transitions weakly and the transitions 5.07/2.35 5.07/2.35 evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 5.07/2.35 5.07/2.35 strictly and produces the following problem: 5.07/2.35 5.07/2.35 3: T: 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ] 5.07/2.35 5.07/2.35 (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 + 1 ] 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 5.07/2.35 5.07/2.35 (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_1 + 1 ] 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (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 ] 5.07/2.35 5.07/2.35 start location: koat_start 5.07/2.35 5.07/2.35 leaf cost: 0 5.07/2.35 5.07/2.35 5.07/2.35 5.07/2.35 A polynomial rank function with 5.07/2.35 5.07/2.35 Pol(evalabcstart) = V_2 5.07/2.35 5.07/2.35 Pol(evalabcbb0in) = V_2 5.07/2.35 5.07/2.35 Pol(evalabc0) = V_2 5.07/2.35 5.07/2.35 Pol(evalabc1) = V_2 5.07/2.35 5.07/2.35 Pol(evalabc2) = V_2 5.07/2.35 5.07/2.35 Pol(evalabc3) = V_2 5.07/2.35 5.07/2.35 Pol(evalabc4) = V_2 5.07/2.35 5.07/2.35 Pol(evalabcbb1in) = -V_1 + V_2 + 1 5.07/2.35 5.07/2.35 Pol(evalabcbb2in) = -V_1 + V_2 5.07/2.35 5.07/2.35 Pol(evalabcbb5in) = -V_1 + V_2 5.07/2.35 5.07/2.35 Pol(evalabcbb3in) = -V_1 + V_2 5.07/2.35 5.07/2.35 Pol(evalabcbb4in) = -V_1 + V_2 5.07/2.35 5.07/2.35 Pol(evalabc8) = V_2 - V_4 + 1 5.07/2.35 5.07/2.35 Pol(evalabc9) = V_2 - V_4 + 1 5.07/2.35 5.07/2.35 Pol(evalabcstop) = -V_1 + V_2 5.07/2.35 5.07/2.35 Pol(koat_start) = V_2 5.07/2.35 5.07/2.35 orients all transitions weakly and the transition 5.07/2.35 5.07/2.35 evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ] 5.07/2.35 5.07/2.35 strictly and produces the following problem: 5.07/2.35 5.07/2.35 4: T: 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ar_1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ] 5.07/2.35 5.07/2.35 (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 + 1 ] 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 5.07/2.35 5.07/2.35 (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_1 + 1 ] 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (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 ] 5.07/2.35 5.07/2.35 start location: koat_start 5.07/2.35 5.07/2.35 leaf cost: 0 5.07/2.35 5.07/2.35 5.07/2.35 5.07/2.35 A polynomial rank function with 5.07/2.35 5.07/2.35 Pol(evalabcbb4in) = 3 5.07/2.35 5.07/2.35 Pol(evalabc8) = 2 5.07/2.35 5.07/2.35 Pol(evalabcbb3in) = 4 5.07/2.35 5.07/2.35 Pol(evalabcbb2in) = 4 5.07/2.35 5.07/2.35 Pol(evalabc9) = 1 5.07/2.35 5.07/2.35 Pol(evalabcbb1in) = 0 5.07/2.35 5.07/2.35 and size complexities 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 5.07/2.35 5.07/2.35 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = ? 5.07/2.35 5.07/2.35 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = ? 5.07/2.35 5.07/2.35 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 5.07/2.35 5.07/2.35 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 5.07/2.35 5.07/2.35 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = ? 5.07/2.35 5.07/2.35 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = ? 5.07/2.35 5.07/2.35 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = ? 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = ? 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ? 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-3) = ? 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-0) = ? 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-3) = ? 5.07/2.35 5.07/2.35 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 + 1 ]", 0-0) = ? 5.07/2.35 5.07/2.35 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 + 1 ]", 0-1) = ar_1 5.07/2.35 5.07/2.35 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 + 1 ]", 0-2) = ? 5.07/2.35 5.07/2.35 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 + 1 ]", 0-3) = ? 5.07/2.35 5.07/2.35 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ? 5.07/2.35 5.07/2.35 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 1 5.07/2.35 5.07/2.35 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = ? 5.07/2.35 5.07/2.35 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-0) = 1 5.07/2.35 5.07/2.35 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.07/2.35 5.07/2.35 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 orients the transitions 5.07/2.35 5.07/2.35 evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 5.07/2.35 5.07/2.35 evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.07/2.35 5.07/2.35 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 5.07/2.35 5.07/2.35 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 5.07/2.35 5.07/2.35 evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 weakly and the transitions 5.07/2.35 5.07/2.35 evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 5.07/2.35 5.07/2.35 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 5.07/2.35 5.07/2.35 evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 strictly and produces the following problem: 5.07/2.35 5.07/2.35 5: T: 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: ar_1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ] 5.07/2.35 5.07/2.35 (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 + 1 ] 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 5.07/2.35 5.07/2.35 (Comp: 4*ar_1, 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_1 + 1 ] 5.07/2.35 5.07/2.35 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 4*ar_1, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 5.07/2.35 5.07/2.35 (Comp: 4*ar_1, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 4*ar_1, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.07/2.35 5.07/2.35 (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 ] 5.07/2.35 5.07/2.35 start location: koat_start 5.07/2.35 5.07/2.35 leaf cost: 0 5.07/2.35 5.07/2.35 5.07/2.35 5.07/2.35 A polynomial rank function with 5.07/2.35 5.07/2.35 Pol(evalabcbb3in) = V_2 - V_3 5.07/2.35 5.07/2.35 Pol(evalabcbb2in) = V_2 - V_3 + 1 5.07/2.35 5.07/2.35 and size complexities 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 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 + 272 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 5.07/2.35 5.07/2.35 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 + 1024 5.07/2.35 5.07/2.35 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = 4*ar_1 + 16 5.07/2.35 5.07/2.35 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = 4*ar_1 + 64 5.07/2.35 5.07/2.35 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-0) = 4*ar_1 + 256 5.07/2.35 5.07/2.35 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-3) = 4*ar_1 + 16 5.07/2.35 5.07/2.35 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = 4*ar_1 + 64 5.07/2.35 5.07/2.35 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = 4*ar_1 + 16 5.07/2.35 5.07/2.35 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 + 16 5.07/2.35 5.07/2.35 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 5.07/2.35 5.07/2.35 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ? 5.07/2.35 5.07/2.35 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 + 1024 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-0) = 4*ar_1 + 16 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-3) = 4*ar_1 + 4*ar_3 + 4096 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-0) = 4*ar_1 + 16 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-2) = ? 5.07/2.35 5.07/2.35 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-3) = 4*ar_1 + 4*ar_3 + 1024 5.07/2.35 5.07/2.35 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 + 1 ]", 0-0) = 4*ar_1 + 68 5.07/2.35 5.07/2.35 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 + 1 ]", 0-1) = ar_1 5.07/2.35 5.07/2.35 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 + 1 ]", 0-2) = ? 5.07/2.35 5.07/2.35 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 + 1 ]", 0-3) = 4*ar_1 + 4*ar_3 + 256 5.07/2.35 5.07/2.35 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = 4*ar_1 + 16 5.07/2.35 5.07/2.35 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 1 5.07/2.35 5.07/2.35 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = 4*ar_1 + 4*ar_3 + 256 5.07/2.35 5.07/2.35 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-0) = 1 5.07/2.35 5.07/2.35 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-1) = ar_1 5.07/2.35 5.07/2.35 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-2) = ar_2 5.07/2.36 5.07/2.36 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-3) = ar_3 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 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 5.07/2.36 5.07/2.36 orients the transitions 5.07/2.36 5.07/2.36 evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.07/2.36 5.07/2.36 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 5.07/2.36 5.07/2.36 weakly and the transition 5.07/2.36 5.07/2.36 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 5.07/2.36 5.07/2.36 strictly and produces the following problem: 5.07/2.36 5.07/2.36 6: T: 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: ar_1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ] 5.07/2.36 5.07/2.36 (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 + 1 ] 5.07/2.36 5.07/2.36 (Comp: ar_1^2 + 2*ar_1, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 5.07/2.36 5.07/2.36 (Comp: 4*ar_1, 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_1 + 1 ] 5.07/2.36 5.07/2.36 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 4*ar_1, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 5.07/2.36 5.07/2.36 (Comp: 4*ar_1, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 4*ar_1, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (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 ] 5.07/2.36 5.07/2.36 start location: koat_start 5.07/2.36 5.07/2.36 leaf cost: 0 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Repeatedly propagating knowledge in problem 6 produces the following problem: 5.07/2.36 5.07/2.36 7: T: 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: ar_1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ] 5.07/2.36 5.07/2.36 (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 + 1 ] 5.07/2.36 5.07/2.36 (Comp: ar_1^2 + 2*ar_1, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 5.07/2.36 5.07/2.36 (Comp: 4*ar_1, 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_1 + 1 ] 5.07/2.36 5.07/2.36 (Comp: ar_1^2 + 2*ar_1, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 4*ar_1, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 5.07/2.36 5.07/2.36 (Comp: 4*ar_1, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 4*ar_1, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 5.07/2.36 5.07/2.36 (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 ] 5.07/2.36 5.07/2.36 start location: koat_start 5.07/2.36 5.07/2.36 leaf cost: 0 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Complexity upper bound 21*ar_1 + 2*ar_1^2 + 11 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Time: 0.181 sec (SMT: 0.138 sec) 5.07/2.36 5.07/2.36 5.07/2.36 ---------------------------------------- 5.07/2.36 5.07/2.36 (2) 5.07/2.36 BOUNDS(1, n^2) 5.07/2.36 5.07/2.36 ---------------------------------------- 5.07/2.36 5.07/2.36 (3) Loat Proof (FINISHED) 5.07/2.36 5.07/2.36 5.07/2.36 ### Pre-processing the ITS problem ### 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Initial linear ITS problem 5.07/2.36 5.07/2.36 Start location: evalabcstart 5.07/2.36 5.07/2.36 0: evalabcstart -> evalabcbb0in : [], cost: 1 5.07/2.36 5.07/2.36 1: evalabcbb0in -> evalabc0 : [], cost: 1 5.07/2.36 5.07/2.36 2: evalabc0 -> evalabc1 : [], cost: 1 5.07/2.36 5.07/2.36 3: evalabc1 -> evalabc2 : [], cost: 1 5.07/2.36 5.07/2.36 4: evalabc2 -> evalabc3 : [], cost: 1 5.07/2.36 5.07/2.36 5: evalabc3 -> evalabc4 : [], cost: 1 5.07/2.36 5.07/2.36 6: evalabc4 -> evalabcbb1in : A'=1, [], cost: 1 5.07/2.36 5.07/2.36 7: evalabcbb1in -> evalabcbb2in : C'=1, [ B>=A ], cost: 1 5.07/2.36 5.07/2.36 8: evalabcbb1in -> evalabcbb5in : [ A>=1+B ], cost: 1 5.07/2.36 5.07/2.36 9: evalabcbb2in -> evalabcbb3in : [ B>=C ], cost: 1 5.07/2.36 5.07/2.36 10: evalabcbb2in -> evalabcbb4in : [ C>=1+B ], cost: 1 5.07/2.36 5.07/2.36 11: evalabcbb3in -> evalabcbb2in : C'=1+C, [], cost: 1 5.07/2.36 5.07/2.36 12: evalabcbb4in -> evalabc8 : D'=1+A, [], cost: 1 5.07/2.36 5.07/2.36 13: evalabc8 -> evalabc9 : [], cost: 1 5.07/2.36 5.07/2.36 14: evalabc9 -> evalabcbb1in : A'=D, [], cost: 1 5.07/2.36 5.07/2.36 15: evalabcbb5in -> evalabcstop : [], cost: 1 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Removed unreachable and leaf rules: 5.07/2.36 5.07/2.36 Start location: evalabcstart 5.07/2.36 5.07/2.36 0: evalabcstart -> evalabcbb0in : [], cost: 1 5.07/2.36 5.07/2.36 1: evalabcbb0in -> evalabc0 : [], cost: 1 5.07/2.36 5.07/2.36 2: evalabc0 -> evalabc1 : [], cost: 1 5.07/2.36 5.07/2.36 3: evalabc1 -> evalabc2 : [], cost: 1 5.07/2.36 5.07/2.36 4: evalabc2 -> evalabc3 : [], cost: 1 5.07/2.36 5.07/2.36 5: evalabc3 -> evalabc4 : [], cost: 1 5.07/2.36 5.07/2.36 6: evalabc4 -> evalabcbb1in : A'=1, [], cost: 1 5.07/2.36 5.07/2.36 7: evalabcbb1in -> evalabcbb2in : C'=1, [ B>=A ], cost: 1 5.07/2.36 5.07/2.36 9: evalabcbb2in -> evalabcbb3in : [ B>=C ], cost: 1 5.07/2.36 5.07/2.36 10: evalabcbb2in -> evalabcbb4in : [ C>=1+B ], cost: 1 5.07/2.36 5.07/2.36 11: evalabcbb3in -> evalabcbb2in : C'=1+C, [], cost: 1 5.07/2.36 5.07/2.36 12: evalabcbb4in -> evalabc8 : D'=1+A, [], cost: 1 5.07/2.36 5.07/2.36 13: evalabc8 -> evalabc9 : [], cost: 1 5.07/2.36 5.07/2.36 14: evalabc9 -> evalabcbb1in : A'=D, [], cost: 1 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 ### Simplification by acceleration and chaining ### 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Eliminated locations (on linear paths): 5.07/2.36 5.07/2.36 Start location: evalabcstart 5.07/2.36 5.07/2.36 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 5.07/2.36 5.07/2.36 7: evalabcbb1in -> evalabcbb2in : C'=1, [ B>=A ], cost: 1 5.07/2.36 5.07/2.36 22: evalabcbb2in -> evalabcbb2in : C'=1+C, [ B>=C ], cost: 2 5.07/2.36 5.07/2.36 25: evalabcbb2in -> evalabcbb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Accelerating simple loops of location 8. 5.07/2.36 5.07/2.36 Accelerating the following rules: 5.07/2.36 5.07/2.36 22: evalabcbb2in -> evalabcbb2in : C'=1+C, [ B>=C ], cost: 2 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Accelerated rule 22 with metering function 1-C+B, yielding the new rule 26. 5.07/2.36 5.07/2.36 Removing the simple loops: 22. 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Accelerated all simple loops using metering functions (where possible): 5.07/2.36 5.07/2.36 Start location: evalabcstart 5.07/2.36 5.07/2.36 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 5.07/2.36 5.07/2.36 7: evalabcbb1in -> evalabcbb2in : C'=1, [ B>=A ], cost: 1 5.07/2.36 5.07/2.36 25: evalabcbb2in -> evalabcbb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 5.07/2.36 5.07/2.36 26: evalabcbb2in -> evalabcbb2in : C'=1+B, [ B>=C ], cost: 2-2*C+2*B 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Chained accelerated rules (with incoming rules): 5.07/2.36 5.07/2.36 Start location: evalabcstart 5.07/2.36 5.07/2.36 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 5.07/2.36 5.07/2.36 7: evalabcbb1in -> evalabcbb2in : C'=1, [ B>=A ], cost: 1 5.07/2.36 5.07/2.36 27: evalabcbb1in -> evalabcbb2in : C'=1+B, [ B>=A && B>=1 ], cost: 1+2*B 5.07/2.36 5.07/2.36 25: evalabcbb2in -> evalabcbb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Eliminated locations (on tree-shaped paths): 5.07/2.36 5.07/2.36 Start location: evalabcstart 5.07/2.36 5.07/2.36 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 5.07/2.36 5.07/2.36 28: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1, D'=1+A, [ B>=A && 1>=1+B ], cost: 5 5.07/2.36 5.07/2.36 29: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1+B, D'=1+A, [ B>=A && B>=1 ], cost: 5+2*B 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Accelerating simple loops of location 7. 5.07/2.36 5.07/2.36 Accelerating the following rules: 5.07/2.36 5.07/2.36 28: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1, D'=1+A, [ B>=A && 1>=1+B ], cost: 5 5.07/2.36 5.07/2.36 29: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1+B, D'=1+A, [ B>=A && B>=1 ], cost: 5+2*B 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Accelerated rule 28 with metering function 1-A+B, yielding the new rule 30. 5.07/2.36 5.07/2.36 Accelerated rule 29 with metering function 1-A+B, yielding the new rule 31. 5.07/2.36 5.07/2.36 Removing the simple loops: 28 29. 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Accelerated all simple loops using metering functions (where possible): 5.07/2.36 5.07/2.36 Start location: evalabcstart 5.07/2.36 5.07/2.36 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 5.07/2.36 5.07/2.36 30: evalabcbb1in -> evalabcbb1in : A'=1+B, C'=1, D'=1+B, [ B>=A && 1>=1+B ], cost: 5-5*A+5*B 5.07/2.36 5.07/2.36 31: evalabcbb1in -> evalabcbb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=A && B>=1 ], cost: 5-5*A-2*(-1+A-B)*B+5*B 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Chained accelerated rules (with incoming rules): 5.07/2.36 5.07/2.36 Start location: evalabcstart 5.07/2.36 5.07/2.36 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 5.07/2.36 5.07/2.36 32: evalabcstart -> evalabcbb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+2*B^2+5*B 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Removed unreachable locations (and leaf rules with constant cost): 5.07/2.36 5.07/2.36 Start location: evalabcstart 5.07/2.36 5.07/2.36 32: evalabcstart -> evalabcbb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+2*B^2+5*B 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 ### Computing asymptotic complexity ### 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Fully simplified ITS problem 5.07/2.36 5.07/2.36 Start location: evalabcstart 5.07/2.36 5.07/2.36 32: evalabcstart -> evalabcbb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+2*B^2+5*B 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Computing asymptotic complexity for rule 32 5.07/2.36 5.07/2.36 Solved the limit problem by the following transformations: 5.07/2.36 5.07/2.36 Created initial limit problem: 5.07/2.36 5.07/2.36 7+2*B^2+5*B (+), B (+/+!) [not solved] 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 removing all constraints (solved by SMT) 5.07/2.36 5.07/2.36 resulting limit problem: [solved] 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 applying transformation rule (C) using substitution {B==n} 5.07/2.36 5.07/2.36 resulting limit problem: 5.07/2.36 5.07/2.36 [solved] 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Solution: 5.07/2.36 5.07/2.36 B / n 5.07/2.36 5.07/2.36 Resulting cost 7+5*n+2*n^2 has complexity: Poly(n^2) 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Found new complexity Poly(n^2). 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 Obtained the following overall complexity (w.r.t. the length of the input n): 5.07/2.36 5.07/2.36 Complexity: Poly(n^2) 5.07/2.36 5.07/2.36 Cpx degree: 2 5.07/2.36 5.07/2.36 Solved cost: 7+5*n+2*n^2 5.07/2.36 5.07/2.36 Rule cost: 7+2*B^2+5*B 5.07/2.36 5.07/2.36 Rule guard: [ B>=1 ] 5.07/2.36 5.07/2.36 5.07/2.36 5.07/2.36 WORST_CASE(Omega(n^2),?) 5.07/2.36 5.07/2.36 5.07/2.36 ---------------------------------------- 5.07/2.36 5.07/2.36 (4) 5.07/2.36 BOUNDS(n^2, INF) 5.24/2.38 EOF