7.00/4.20 WORST_CASE(Omega(n^1), O(n^2)) 7.10/4.21 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 7.10/4.21 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.10/4.21 7.10/4.21 7.10/4.21 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). 7.10/4.21 7.10/4.21 (0) CpxIntTrs 7.10/4.21 (1) Koat Proof [FINISHED, 118 ms] 7.10/4.21 (2) BOUNDS(1, n^2) 7.10/4.21 (3) Loat Proof [FINISHED, 623 ms] 7.10/4.21 (4) BOUNDS(n^1, INF) 7.10/4.21 7.10/4.21 7.10/4.21 ---------------------------------------- 7.10/4.21 7.10/4.21 (0) 7.10/4.21 Obligation: 7.10/4.21 Complexity Int TRS consisting of the following rules: 7.10/4.21 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 7.10/4.21 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 7.10/4.21 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 7.10/4.21 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 7.10/4.21 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 7.10/4.21 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 7.10/4.21 eval_abc_4(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb1_in(v_3, 0, v_j_0, v_n)) :|: TRUE 7.10/4.21 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, 0, v_n)) :|: v_i_0 <= v_n 7.10/4.21 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 7.10/4.21 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 7.10/4.21 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 7.10/4.21 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 + 2, v_n)) :|: TRUE 7.10/4.21 eval_abc_bb4_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_8(v_i_0 + 2, v_i_0, v_j_0, v_n)) :|: TRUE 7.10/4.21 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 7.10/4.21 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 7.10/4.21 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 7.10/4.21 7.10/4.21 The start-symbols are:[eval_abc_start_4] 7.10/4.21 7.10/4.21 7.10/4.21 ---------------------------------------- 7.10/4.21 7.10/4.21 (1) Koat Proof (FINISHED) 7.10/4.21 YES(?, 23*ar_1 + 2*ar_1^2 + 32) 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Initial complexity problem: 7.10/4.21 7.10/4.21 1: T: 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 start location: koat_start 7.10/4.21 7.10/4.21 leaf cost: 0 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Repeatedly propagating knowledge in problem 1 produces the following problem: 7.10/4.21 7.10/4.21 2: T: 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 start location: koat_start 7.10/4.21 7.10/4.21 leaf cost: 0 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 A polynomial rank function with 7.10/4.21 7.10/4.21 Pol(evalabcstart) = 2 7.10/4.21 7.10/4.21 Pol(evalabcbb0in) = 2 7.10/4.21 7.10/4.21 Pol(evalabc0) = 2 7.10/4.21 7.10/4.21 Pol(evalabc1) = 2 7.10/4.21 7.10/4.21 Pol(evalabc2) = 2 7.10/4.21 7.10/4.21 Pol(evalabc3) = 2 7.10/4.21 7.10/4.21 Pol(evalabc4) = 2 7.10/4.21 7.10/4.21 Pol(evalabcbb1in) = 2 7.10/4.21 7.10/4.21 Pol(evalabcbb2in) = 2 7.10/4.21 7.10/4.21 Pol(evalabcbb5in) = 1 7.10/4.21 7.10/4.21 Pol(evalabcbb3in) = 2 7.10/4.21 7.10/4.21 Pol(evalabcbb4in) = 2 7.10/4.21 7.10/4.21 Pol(evalabc8) = 2 7.10/4.21 7.10/4.21 Pol(evalabc9) = 2 7.10/4.21 7.10/4.21 Pol(evalabcstop) = 0 7.10/4.21 7.10/4.21 Pol(koat_start) = 2 7.10/4.21 7.10/4.21 orients all transitions weakly and the transitions 7.10/4.21 7.10/4.21 evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 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 ] 7.10/4.21 7.10/4.21 strictly and produces the following problem: 7.10/4.21 7.10/4.21 3: T: 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 start location: koat_start 7.10/4.21 7.10/4.21 leaf cost: 0 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 A polynomial rank function with 7.10/4.21 7.10/4.21 Pol(evalabcstart) = V_2 + 1 7.10/4.21 7.10/4.21 Pol(evalabcbb0in) = V_2 + 1 7.10/4.21 7.10/4.21 Pol(evalabc0) = V_2 + 1 7.10/4.21 7.10/4.21 Pol(evalabc1) = V_2 + 1 7.10/4.21 7.10/4.21 Pol(evalabc2) = V_2 + 1 7.10/4.21 7.10/4.21 Pol(evalabc3) = V_2 + 1 7.10/4.21 7.10/4.21 Pol(evalabc4) = V_2 + 1 7.10/4.21 7.10/4.21 Pol(evalabcbb1in) = -V_1 + V_2 + 1 7.10/4.21 7.10/4.21 Pol(evalabcbb2in) = -V_1 + V_2 - 1 7.10/4.21 7.10/4.21 Pol(evalabcbb5in) = -V_1 + V_2 7.10/4.21 7.10/4.21 Pol(evalabcbb3in) = -V_1 + V_2 - 1 7.10/4.21 7.10/4.21 Pol(evalabcbb4in) = -V_1 + V_2 - 1 7.10/4.21 7.10/4.21 Pol(evalabc8) = V_2 - V_4 + 1 7.10/4.21 7.10/4.21 Pol(evalabc9) = V_2 - V_4 + 1 7.10/4.21 7.10/4.21 Pol(evalabcstop) = -V_1 + V_2 7.10/4.21 7.10/4.21 Pol(koat_start) = V_2 + 1 7.10/4.21 7.10/4.21 orients all transitions weakly and the transition 7.10/4.21 7.10/4.21 evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 ] 7.10/4.21 7.10/4.21 strictly and produces the following problem: 7.10/4.21 7.10/4.21 4: T: 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 start location: koat_start 7.10/4.21 7.10/4.21 leaf cost: 0 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 A polynomial rank function with 7.10/4.21 7.10/4.21 Pol(evalabcbb4in) = 3 7.10/4.21 7.10/4.21 Pol(evalabc8) = 2 7.10/4.21 7.10/4.21 Pol(evalabcbb3in) = 4 7.10/4.21 7.10/4.21 Pol(evalabcbb2in) = 4 7.10/4.21 7.10/4.21 Pol(evalabc9) = 1 7.10/4.21 7.10/4.21 Pol(evalabcbb1in) = 0 7.10/4.21 7.10/4.21 and size complexities 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 7.10/4.21 7.10/4.21 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 7.10/4.21 7.10/4.21 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = ? 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ? 7.10/4.21 7.10/4.21 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = ? 7.10/4.21 7.10/4.21 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 7.10/4.21 7.10/4.21 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 7.10/4.21 7.10/4.21 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2))", 0-0) = ? 7.10/4.21 7.10/4.21 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2))", 0-1) = ar_1 7.10/4.21 7.10/4.21 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2))", 0-2) = ? 7.10/4.21 7.10/4.21 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2))", 0-3) = ? 7.10/4.21 7.10/4.21 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3))", 0-0) = ? 7.10/4.21 7.10/4.21 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3))", 0-1) = ar_1 7.10/4.21 7.10/4.21 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3))", 0-2) = ? 7.10/4.21 7.10/4.21 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3))", 0-3) = ? 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ? 7.10/4.21 7.10/4.21 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ar_1 7.10/4.21 7.10/4.21 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 0 7.10/4.21 7.10/4.21 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = ? 7.10/4.21 7.10/4.21 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-0) = 0 7.10/4.21 7.10/4.21 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-1) = ar_1 7.10/4.21 7.10/4.21 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-2) = ar_2 7.10/4.21 7.10/4.21 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-3) = ar_3 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 orients the transitions 7.10/4.21 7.10/4.21 evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2)) 7.10/4.21 7.10/4.21 evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3)) 7.10/4.21 7.10/4.21 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 ] 7.10/4.21 7.10/4.21 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 7.10/4.21 7.10/4.21 evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 weakly and the transitions 7.10/4.21 7.10/4.21 evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2)) 7.10/4.21 7.10/4.21 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 ] 7.10/4.21 7.10/4.21 evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 strictly and produces the following problem: 7.10/4.21 7.10/4.21 5: T: 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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_1 + 1 ] 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 4*ar_1 + 4, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2)) 7.10/4.21 7.10/4.21 (Comp: 4*ar_1 + 4, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 4*ar_1 + 4, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 start location: koat_start 7.10/4.21 7.10/4.21 leaf cost: 0 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 A polynomial rank function with 7.10/4.21 7.10/4.21 Pol(evalabcbb3in) = V_2 - V_3 7.10/4.21 7.10/4.21 Pol(evalabcbb2in) = V_2 - V_3 + 2 7.10/4.21 7.10/4.21 and size complexities 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 8*ar_1 + 32768 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 7.10/4.21 7.10/4.21 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = 8*ar_1 + 8*ar_3 + 262144 7.10/4.21 7.10/4.21 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = 8*ar_1 + 512 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ? 7.10/4.21 7.10/4.21 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = 8*ar_1 + 4096 7.10/4.21 7.10/4.21 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-0) = 8*ar_1 + 32768 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 7.10/4.21 7.10/4.21 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-3) = 8*ar_1 + 512 7.10/4.21 7.10/4.21 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2))", 0-0) = 8*ar_1 + 4096 7.10/4.21 7.10/4.21 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2))", 0-1) = ar_1 7.10/4.21 7.10/4.21 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2))", 0-2) = ? 7.10/4.21 7.10/4.21 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2))", 0-3) = 8*ar_1 + 512 7.10/4.21 7.10/4.21 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3))", 0-0) = 8*ar_1 + 512 7.10/4.21 7.10/4.21 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3))", 0-1) = ar_1 7.10/4.21 7.10/4.21 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3))", 0-2) = ? 7.10/4.21 7.10/4.21 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3))", 0-3) = 8*ar_1 + 8*ar_3 + 262144 7.10/4.21 7.10/4.21 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) = 8*ar_1 + 512 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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) = 8*ar_1 + 8*ar_3 + 2097152 7.10/4.21 7.10/4.21 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) = 8*ar_1 + 512 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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) = 8*ar_1 + 8*ar_3 + 262144 7.10/4.21 7.10/4.21 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) = 8*ar_1 + 4096 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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) = ? 7.10/4.21 7.10/4.21 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) = 8*ar_1 + 8*ar_3 + 32768 7.10/4.21 7.10/4.21 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = 8*ar_1 + 512 7.10/4.21 7.10/4.21 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ar_1 7.10/4.21 7.10/4.21 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 0 7.10/4.21 7.10/4.21 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, 0, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = 8*ar_1 + 8*ar_3 + 32768 7.10/4.21 7.10/4.21 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-0) = 0 7.10/4.21 7.10/4.21 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-1) = ar_1 7.10/4.21 7.10/4.21 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-2) = ar_2 7.10/4.21 7.10/4.21 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3))", 0-3) = ar_3 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 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 7.10/4.21 7.10/4.21 orients the transitions 7.10/4.21 7.10/4.21 evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3)) 7.10/4.21 7.10/4.21 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 7.10/4.21 7.10/4.21 weakly and the transition 7.10/4.21 7.10/4.21 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 7.10/4.21 7.10/4.21 strictly and produces the following problem: 7.10/4.21 7.10/4.21 6: T: 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (Comp: ar_1^2 + 3*ar_1 + 2, 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 ] 7.10/4.21 7.10/4.21 (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_1 + 1 ] 7.10/4.21 7.10/4.21 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 4*ar_1 + 4, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2)) 7.10/4.21 7.10/4.21 (Comp: 4*ar_1 + 4, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 4*ar_1 + 4, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 start location: koat_start 7.10/4.21 7.10/4.21 leaf cost: 0 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Repeatedly propagating knowledge in problem 6 produces the following problem: 7.10/4.21 7.10/4.21 7: T: 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 (Comp: ar_1^2 + 3*ar_1 + 2, 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 ] 7.10/4.21 7.10/4.21 (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_1 + 1 ] 7.10/4.21 7.10/4.21 (Comp: ar_1^2 + 3*ar_1 + 2, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 4*ar_1 + 4, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 2)) 7.10/4.21 7.10/4.21 (Comp: 4*ar_1 + 4, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 4*ar_1 + 4, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 7.10/4.21 7.10/4.21 (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 ] 7.10/4.21 7.10/4.21 start location: koat_start 7.10/4.21 7.10/4.21 leaf cost: 0 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Complexity upper bound 23*ar_1 + 2*ar_1^2 + 32 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Time: 0.176 sec (SMT: 0.133 sec) 7.10/4.21 7.10/4.21 7.10/4.21 ---------------------------------------- 7.10/4.21 7.10/4.21 (2) 7.10/4.21 BOUNDS(1, n^2) 7.10/4.21 7.10/4.21 ---------------------------------------- 7.10/4.21 7.10/4.21 (3) Loat Proof (FINISHED) 7.10/4.21 7.10/4.21 7.10/4.21 ### Pre-processing the ITS problem ### 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Initial linear ITS problem 7.10/4.21 7.10/4.21 Start location: evalabcstart 7.10/4.21 7.10/4.21 0: evalabcstart -> evalabcbb0in : [], cost: 1 7.10/4.21 7.10/4.21 1: evalabcbb0in -> evalabc0 : [], cost: 1 7.10/4.21 7.10/4.21 2: evalabc0 -> evalabc1 : [], cost: 1 7.10/4.21 7.10/4.21 3: evalabc1 -> evalabc2 : [], cost: 1 7.10/4.21 7.10/4.21 4: evalabc2 -> evalabc3 : [], cost: 1 7.10/4.21 7.10/4.21 5: evalabc3 -> evalabc4 : [], cost: 1 7.10/4.21 7.10/4.21 6: evalabc4 -> evalabcbb1in : A'=0, [], cost: 1 7.10/4.21 7.10/4.21 7: evalabcbb1in -> evalabcbb2in : C'=0, [ B>=A ], cost: 1 7.10/4.21 7.10/4.21 8: evalabcbb1in -> evalabcbb5in : [ A>=1+B ], cost: 1 7.10/4.21 7.10/4.21 9: evalabcbb2in -> evalabcbb3in : [ B>=C ], cost: 1 7.10/4.21 7.10/4.21 10: evalabcbb2in -> evalabcbb4in : [ C>=1+B ], cost: 1 7.10/4.21 7.10/4.21 11: evalabcbb3in -> evalabcbb2in : C'=2+C, [], cost: 1 7.10/4.21 7.10/4.21 12: evalabcbb4in -> evalabc8 : D'=2+A, [], cost: 1 7.10/4.21 7.10/4.21 13: evalabc8 -> evalabc9 : [], cost: 1 7.10/4.21 7.10/4.21 14: evalabc9 -> evalabcbb1in : A'=D, [], cost: 1 7.10/4.21 7.10/4.21 15: evalabcbb5in -> evalabcstop : [], cost: 1 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Removed unreachable and leaf rules: 7.10/4.21 7.10/4.21 Start location: evalabcstart 7.10/4.21 7.10/4.21 0: evalabcstart -> evalabcbb0in : [], cost: 1 7.10/4.21 7.10/4.21 1: evalabcbb0in -> evalabc0 : [], cost: 1 7.10/4.21 7.10/4.21 2: evalabc0 -> evalabc1 : [], cost: 1 7.10/4.21 7.10/4.21 3: evalabc1 -> evalabc2 : [], cost: 1 7.10/4.21 7.10/4.21 4: evalabc2 -> evalabc3 : [], cost: 1 7.10/4.21 7.10/4.21 5: evalabc3 -> evalabc4 : [], cost: 1 7.10/4.21 7.10/4.21 6: evalabc4 -> evalabcbb1in : A'=0, [], cost: 1 7.10/4.21 7.10/4.21 7: evalabcbb1in -> evalabcbb2in : C'=0, [ B>=A ], cost: 1 7.10/4.21 7.10/4.21 9: evalabcbb2in -> evalabcbb3in : [ B>=C ], cost: 1 7.10/4.21 7.10/4.21 10: evalabcbb2in -> evalabcbb4in : [ C>=1+B ], cost: 1 7.10/4.21 7.10/4.21 11: evalabcbb3in -> evalabcbb2in : C'=2+C, [], cost: 1 7.10/4.21 7.10/4.21 12: evalabcbb4in -> evalabc8 : D'=2+A, [], cost: 1 7.10/4.21 7.10/4.21 13: evalabc8 -> evalabc9 : [], cost: 1 7.10/4.21 7.10/4.21 14: evalabc9 -> evalabcbb1in : A'=D, [], cost: 1 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 ### Simplification by acceleration and chaining ### 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Eliminated locations (on linear paths): 7.10/4.21 7.10/4.21 Start location: evalabcstart 7.10/4.21 7.10/4.21 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 7.10/4.21 7.10/4.21 7: evalabcbb1in -> evalabcbb2in : C'=0, [ B>=A ], cost: 1 7.10/4.21 7.10/4.21 22: evalabcbb2in -> evalabcbb2in : C'=2+C, [ B>=C ], cost: 2 7.10/4.21 7.10/4.21 25: evalabcbb2in -> evalabcbb1in : A'=2+A, D'=2+A, [ C>=1+B ], cost: 4 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Accelerating simple loops of location 8. 7.10/4.21 7.10/4.21 Accelerating the following rules: 7.10/4.21 7.10/4.21 22: evalabcbb2in -> evalabcbb2in : C'=2+C, [ B>=C ], cost: 2 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Accelerated rule 22 with metering function meter (where 2*meter==-C+B), yielding the new rule 26. 7.10/4.21 7.10/4.21 Removing the simple loops: 22. 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Accelerated all simple loops using metering functions (where possible): 7.10/4.21 7.10/4.21 Start location: evalabcstart 7.10/4.21 7.10/4.21 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 7.10/4.21 7.10/4.21 7: evalabcbb1in -> evalabcbb2in : C'=0, [ B>=A ], cost: 1 7.10/4.21 7.10/4.21 25: evalabcbb2in -> evalabcbb1in : A'=2+A, D'=2+A, [ C>=1+B ], cost: 4 7.10/4.21 7.10/4.21 26: evalabcbb2in -> evalabcbb2in : C'=2*meter+C, [ B>=C && 2*meter==-C+B && meter>=1 ], cost: 2*meter 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Chained accelerated rules (with incoming rules): 7.10/4.21 7.10/4.21 Start location: evalabcstart 7.10/4.21 7.10/4.21 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 7.10/4.21 7.10/4.21 7: evalabcbb1in -> evalabcbb2in : C'=0, [ B>=A ], cost: 1 7.10/4.21 7.10/4.21 27: evalabcbb1in -> evalabcbb2in : C'=2*meter, [ B>=A && B>=0 && 2*meter==B && meter>=1 ], cost: 1+2*meter 7.10/4.21 7.10/4.21 25: evalabcbb2in -> evalabcbb1in : A'=2+A, D'=2+A, [ C>=1+B ], cost: 4 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Eliminated locations (on tree-shaped paths): 7.10/4.21 7.10/4.21 Start location: evalabcstart 7.10/4.21 7.10/4.21 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 7.10/4.21 7.10/4.21 28: evalabcbb1in -> evalabcbb1in : A'=2+A, C'=0, D'=2+A, [ B>=A && 0>=1+B ], cost: 5 7.10/4.21 7.10/4.21 29: evalabcbb1in -> [16] : [ B>=A && B>=0 && 2*meter==B && meter>=1 ], cost: 1+2*meter 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Accelerating simple loops of location 7. 7.10/4.21 7.10/4.21 Accelerating the following rules: 7.10/4.21 7.10/4.21 28: evalabcbb1in -> evalabcbb1in : A'=2+A, C'=0, D'=2+A, [ B>=A && 0>=1+B ], cost: 5 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Accelerated rule 28 with metering function meter_1 (where 2*meter_1==-A+B), yielding the new rule 30. 7.10/4.21 7.10/4.21 Removing the simple loops: 28. 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Accelerated all simple loops using metering functions (where possible): 7.10/4.21 7.10/4.21 Start location: evalabcstart 7.10/4.21 7.10/4.21 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 7.10/4.21 7.10/4.21 29: evalabcbb1in -> [16] : [ B>=A && B>=0 && 2*meter==B && meter>=1 ], cost: 1+2*meter 7.10/4.21 7.10/4.21 30: evalabcbb1in -> evalabcbb1in : A'=A+2*meter_1, C'=0, D'=A+2*meter_1, [ B>=A && 0>=1+B && 2*meter_1==-A+B && meter_1>=1 ], cost: 5*meter_1 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Chained accelerated rules (with incoming rules): 7.10/4.21 7.10/4.21 Start location: evalabcstart 7.10/4.21 7.10/4.21 21: evalabcstart -> evalabcbb1in : A'=0, [], cost: 7 7.10/4.21 7.10/4.21 29: evalabcbb1in -> [16] : [ B>=A && B>=0 && 2*meter==B && meter>=1 ], cost: 1+2*meter 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Eliminated locations (on linear paths): 7.10/4.21 7.10/4.21 Start location: evalabcstart 7.10/4.21 7.10/4.21 31: evalabcstart -> [16] : A'=0, [ B>=0 && 2*meter==B && meter>=1 ], cost: 8+2*meter 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 ### Computing asymptotic complexity ### 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Fully simplified ITS problem 7.10/4.21 7.10/4.21 Start location: evalabcstart 7.10/4.21 7.10/4.21 31: evalabcstart -> [16] : A'=0, [ B>=0 && 2*meter==B && meter>=1 ], cost: 8+2*meter 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Computing asymptotic complexity for rule 31 7.10/4.21 7.10/4.21 Simplified the guard: 7.10/4.21 7.10/4.21 31: evalabcstart -> [16] : A'=0, [ 2*meter==B && meter>=1 ], cost: 8+2*meter 7.10/4.21 7.10/4.21 Solved the limit problem by the following transformations: 7.10/4.21 7.10/4.21 Created initial limit problem: 7.10/4.21 7.10/4.21 meter (+/+!), 1-2*meter+B (+/+!), 1+2*meter-B (+/+!), 8+2*meter (+) [not solved] 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 applying transformation rule (C) using substitution {B==2*meter} 7.10/4.21 7.10/4.21 resulting limit problem: 7.10/4.21 7.10/4.21 1 (+/+!), meter (+/+!), 8+2*meter (+) [not solved] 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 applying transformation rule (B), deleting 1 (+/+!) 7.10/4.21 7.10/4.21 resulting limit problem: 7.10/4.21 7.10/4.21 meter (+/+!), 8+2*meter (+) [not solved] 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 removing all constraints (solved by SMT) 7.10/4.21 7.10/4.21 resulting limit problem: [solved] 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 applying transformation rule (C) using substitution {meter==n} 7.10/4.21 7.10/4.21 resulting limit problem: 7.10/4.21 7.10/4.21 [solved] 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Solution: 7.10/4.21 7.10/4.21 meter / n 7.10/4.21 7.10/4.21 B / 2*n 7.10/4.21 7.10/4.21 Resulting cost 8+2*n has complexity: Poly(n^1) 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Found new complexity Poly(n^1). 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 Obtained the following overall complexity (w.r.t. the length of the input n): 7.10/4.21 7.10/4.21 Complexity: Poly(n^1) 7.10/4.21 7.10/4.21 Cpx degree: 1 7.10/4.21 7.10/4.21 Solved cost: 8+2*n 7.10/4.21 7.10/4.21 Rule cost: 8+2*meter 7.10/4.21 7.10/4.21 Rule guard: [ 2*meter==B && meter>=1 ] 7.10/4.21 7.10/4.21 7.10/4.21 7.10/4.21 WORST_CASE(Omega(n^1),?) 7.10/4.21 7.10/4.21 7.10/4.21 ---------------------------------------- 7.10/4.21 7.10/4.21 (4) 7.10/4.21 BOUNDS(n^1, INF) 7.10/4.24 EOF