YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. eval_speedpldi3_start(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb0_in(v_i_0,v_j_0,v_m,v_n) True (1,1) 1. eval_speedpldi3_bb0_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_0(v_i_0,v_j_0,v_m,v_n) True (?,1) 2. eval_speedpldi3_0(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_1(v_i_0,v_j_0,v_m,v_n) True (?,1) 3. eval_speedpldi3_1(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) True (?,1) 4. eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [0 >= v_m] (?,1) 5. eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [v_m >= v_n] (?,1) 6. eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(0,0,v_m,v_n) [-1 + v_m >= 0 && -1 + v_n >= v_m] (?,1) 7. eval_speedpldi3_bb1_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) [-2 + v_n >= 0 (?,1) && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_n >= v_i_0] 8. eval_speedpldi3_bb1_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [-2 + v_n >= 0 (?,1) && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && v_i_0 >= v_n] 9. eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(v_i_0,1 + v_j_0,v_m,v_n) [-2 + v_n >= 0 (?,1) && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_m >= v_j_0] 10. eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(1 + v_i_0,0,v_m,v_n) [-2 + v_n >= 0 (?,1) && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && v_j_0 >= v_m] 11. eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_stop(v_i_0,v_j_0,v_m,v_n) True (?,1) Signature: {(eval_speedpldi3_0,4) ;(eval_speedpldi3_1,4) ;(eval_speedpldi3_2,4) ;(eval_speedpldi3_bb0_in,4) ;(eval_speedpldi3_bb1_in,4) ;(eval_speedpldi3_bb2_in,4) ;(eval_speedpldi3_bb3_in,4) ;(eval_speedpldi3_start,4) ;(eval_speedpldi3_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{11},5->{11},6->{7,8},7->{9,10},8->{11},9->{7,8},10->{7,8},11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(6,8),(9,8)] * Step 2: FromIts YES + Considered Problem: Rules: 0. eval_speedpldi3_start(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb0_in(v_i_0,v_j_0,v_m,v_n) True (1,1) 1. eval_speedpldi3_bb0_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_0(v_i_0,v_j_0,v_m,v_n) True (?,1) 2. eval_speedpldi3_0(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_1(v_i_0,v_j_0,v_m,v_n) True (?,1) 3. eval_speedpldi3_1(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) True (?,1) 4. eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [0 >= v_m] (?,1) 5. eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [v_m >= v_n] (?,1) 6. eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(0,0,v_m,v_n) [-1 + v_m >= 0 && -1 + v_n >= v_m] (?,1) 7. eval_speedpldi3_bb1_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) [-2 + v_n >= 0 (?,1) && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_n >= v_i_0] 8. eval_speedpldi3_bb1_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [-2 + v_n >= 0 (?,1) && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && v_i_0 >= v_n] 9. eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(v_i_0,1 + v_j_0,v_m,v_n) [-2 + v_n >= 0 (?,1) && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_m >= v_j_0] 10. eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(1 + v_i_0,0,v_m,v_n) [-2 + v_n >= 0 (?,1) && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && v_j_0 >= v_m] 11. eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_stop(v_i_0,v_j_0,v_m,v_n) True (?,1) Signature: {(eval_speedpldi3_0,4) ;(eval_speedpldi3_1,4) ;(eval_speedpldi3_2,4) ;(eval_speedpldi3_bb0_in,4) ;(eval_speedpldi3_bb1_in,4) ;(eval_speedpldi3_bb2_in,4) ;(eval_speedpldi3_bb3_in,4) ;(eval_speedpldi3_start,4) ;(eval_speedpldi3_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{11},5->{11},6->{7},7->{9,10},8->{11},9->{7},10->{7,8},11->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: eval_speedpldi3_start(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb0_in(v_i_0,v_j_0,v_m,v_n) True eval_speedpldi3_bb0_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_0(v_i_0,v_j_0,v_m,v_n) True eval_speedpldi3_0(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_1(v_i_0,v_j_0,v_m,v_n) True eval_speedpldi3_1(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) True eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [0 >= v_m] eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [v_m >= v_n] eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(0,0,v_m,v_n) [-1 + v_m >= 0 && -1 + v_n >= v_m] eval_speedpldi3_bb1_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) [-2 + v_n >= 0 && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_n >= v_i_0] eval_speedpldi3_bb1_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [-2 + v_n >= 0 && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && v_i_0 >= v_n] eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(v_i_0,1 + v_j_0,v_m,v_n) [-2 + v_n >= 0 && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_m >= v_j_0] eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(1 + v_i_0,0,v_m,v_n) [-2 + v_n >= 0 && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && v_j_0 >= v_m] eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_stop(v_i_0,v_j_0,v_m,v_n) True Signature: {(eval_speedpldi3_0,4) ;(eval_speedpldi3_1,4) ;(eval_speedpldi3_2,4) ;(eval_speedpldi3_bb0_in,4) ;(eval_speedpldi3_bb1_in,4) ;(eval_speedpldi3_bb2_in,4) ;(eval_speedpldi3_bb3_in,4) ;(eval_speedpldi3_start,4) ;(eval_speedpldi3_stop,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{11},5->{11},6->{7},7->{9,10},8->{11},9->{7},10->{7,8},11->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[7,9,10] c: [10] | `- p:[7,9] c: [7,9] * Step 4: CloseWith YES + Considered Problem: (Rules: eval_speedpldi3_start(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb0_in(v_i_0,v_j_0,v_m,v_n) True eval_speedpldi3_bb0_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_0(v_i_0,v_j_0,v_m,v_n) True eval_speedpldi3_0(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_1(v_i_0,v_j_0,v_m,v_n) True eval_speedpldi3_1(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) True eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [0 >= v_m] eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [v_m >= v_n] eval_speedpldi3_2(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(0,0,v_m,v_n) [-1 + v_m >= 0 && -1 + v_n >= v_m] eval_speedpldi3_bb1_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) [-2 + v_n >= 0 && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_n >= v_i_0] eval_speedpldi3_bb1_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) [-2 + v_n >= 0 && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && v_i_0 >= v_n] eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(v_i_0,1 + v_j_0,v_m,v_n) [-2 + v_n >= 0 && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_m >= v_j_0] eval_speedpldi3_bb2_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_bb1_in(1 + v_i_0,0,v_m,v_n) [-2 + v_n >= 0 && -3 + v_m + v_n >= 0 && -1 + -1*v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_j_0 + v_m >= 0 && -1 + v_i_0 + v_m >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && v_j_0 >= v_m] eval_speedpldi3_bb3_in(v_i_0,v_j_0,v_m,v_n) -> eval_speedpldi3_stop(v_i_0,v_j_0,v_m,v_n) True Signature: {(eval_speedpldi3_0,4) ;(eval_speedpldi3_1,4) ;(eval_speedpldi3_2,4) ;(eval_speedpldi3_bb0_in,4) ;(eval_speedpldi3_bb1_in,4) ;(eval_speedpldi3_bb2_in,4) ;(eval_speedpldi3_bb3_in,4) ;(eval_speedpldi3_start,4) ;(eval_speedpldi3_stop,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{11},5->{11},6->{7},7->{9,10},8->{11},9->{7},10->{7,8},11->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[7,9,10] c: [10] | `- p:[7,9] c: [7,9]) + Applied Processor: CloseWith True + Details: () YES