NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f1549_0_search_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 && 0==arg1P_1 ], cost: 1 1: f1549_0_search_LT -> f1911_0_search_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1 f1944_0_displayChessboard_GE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1>=x15_1 && 0==arg1P_6 ], cost: 1 2: f1911_0_search_GE -> f1911_0_search_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg20 && arg1==arg1P_3 && 1+arg2==arg2P_3 ], cost: 1 3: f1911_0_search_GE -> f1549_0_search_LT : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ x7_1>0 && arg20 && arg1>-1 && arg1arg1 && 1+arg1==arg1P_4 ], cost: 1 4: f1911_0_search_GE -> f1911_0_search_GE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ x11_1>0 && arg20 && arg1>-1 && arg1arg1 && arg1==arg1P_5 && 1+arg2==arg2P_5 ], cost: 1 11: f1911_0_search_GE -> f1876_0_safeMove_GE : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg20 && 1==arg1P_12 && 0==arg2P_12 && arg1==arg3P_12 ], cost: 1 6: f1944_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1 f1944_0_displayChessboard_GE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg2>=x19_1 && 1+arg1==arg1P_8 ], cost: 1 8: f2167_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ x25_1 f2167_0_displayChessboard_GE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ x46_1>arg2 && arg2 f2167_0_displayChessboard_GE : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2 f1969_0_safeMove_NE : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>0 && x32_1>0 && arg1>0 && arg2arg2 && arg3==arg1P_13 && arg2==arg2P_13 && 1==arg3P_13 ], cost: 1 13: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg3>0 && x36_1>0 && arg1>0 && arg2arg2 && arg3==arg1P_14 && arg2==arg2P_14 && 0==arg3P_14 ], cost: 1 14: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg3>arg2 && 0==arg1 && 0==arg1P_15 && 1+arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1 15: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ 1==arg3 && 0==arg1P_16 && 1+arg2==arg2P_16 && arg1==arg3P_16 ], cost: 1 16: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ 0==arg3 && 1==arg1P_17 && 1+arg2==arg2P_17 && arg1==arg3P_17 ], cost: 1 17: __init -> f1_0_main_Load : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 17: __init -> f1_0_main_Load : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f1549_0_search_LT -> f1911_0_search_GE : arg2'=0, arg3'=arg3P_2, [], cost: 1 5: f1549_0_search_LT -> f1944_0_displayChessboard_GE : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 2: f1911_0_search_GE -> f1911_0_search_GE : arg2'=1+arg2, arg3'=arg3P_3, [], cost: 1 3: f1911_0_search_GE -> f1549_0_search_LT : arg1'=1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 1 4: f1911_0_search_GE -> f1911_0_search_GE : arg2'=1+arg2, arg3'=arg3P_5, [ arg1>-1 ], cost: 1 11: f1911_0_search_GE -> f1876_0_safeMove_GE : arg1'=1, arg2'=0, arg3'=arg1, [], cost: 1 6: f1944_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg2'=0, arg3'=arg3P_7, [], cost: 1 7: f2167_0_displayChessboard_GE -> f1944_0_displayChessboard_GE : arg1'=1+arg1, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 8: f2167_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg2'=1+arg2, arg3'=arg3P_9, [], cost: 1 9: f2167_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg2'=1+arg2, arg3'=arg3P_10, [], cost: 1 10: f2167_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg2'=1+arg2, arg3'=arg3P_11, [], cost: 1 12: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=1, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 13: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=0, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 14: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, [ arg3>arg2 && 0==arg1 ], cost: 1 15: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, arg3'=arg1, [ 1==arg3 ], cost: 1 16: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=1, arg2'=1+arg2, arg3'=arg1, [ 0==arg3 ], cost: 1 17: __init -> f1_0_main_Load : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 2: f1911_0_search_GE -> f1911_0_search_GE : arg2'=1+arg2, arg3'=arg3P_3, [], cost: 1 4: f1911_0_search_GE -> f1911_0_search_GE : arg2'=1+arg2, arg3'=arg3P_5, [ arg1>-1 ], cost: 1 Accelerated rule 2 with NONTERM, yielding the new rule 18. Accelerated rule 4 with NONTERM, yielding the new rule 19. Removing the simple loops: 2 4. Accelerating simple loops of location 4. Accelerating the following rules: 8: f2167_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg2'=1+arg2, arg3'=arg3P_9, [], cost: 1 9: f2167_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg2'=1+arg2, arg3'=arg3P_10, [], cost: 1 10: f2167_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg2'=1+arg2, arg3'=arg3P_11, [], cost: 1 Accelerated rule 8 with NONTERM, yielding the new rule 20. Accelerated rule 9 with NONTERM, yielding the new rule 21. Accelerated rule 10 with NONTERM, yielding the new rule 22. Removing the simple loops: 8 9 10. Also removing duplicate rules: 20 21. Accelerating simple loops of location 5. Accelerating the following rules: 14: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, [ arg3>arg2 && 0==arg1 ], cost: 1 Accelerated rule 14 with metering function arg3-arg2, yielding the new rule 23. Removing the simple loops: 14. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f1549_0_search_LT -> f1911_0_search_GE : arg2'=0, arg3'=arg3P_2, [], cost: 1 5: f1549_0_search_LT -> f1944_0_displayChessboard_GE : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 3: f1911_0_search_GE -> f1549_0_search_LT : arg1'=1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 1 11: f1911_0_search_GE -> f1876_0_safeMove_GE : arg1'=1, arg2'=0, arg3'=arg1, [], cost: 1 18: f1911_0_search_GE -> [8] : [], cost: NONTERM 19: f1911_0_search_GE -> [8] : [ arg1>-1 ], cost: NONTERM 6: f1944_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg2'=0, arg3'=arg3P_7, [], cost: 1 7: f2167_0_displayChessboard_GE -> f1944_0_displayChessboard_GE : arg1'=1+arg1, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 22: f2167_0_displayChessboard_GE -> [9] : [], cost: NONTERM 12: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=1, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 13: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=0, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 23: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg3, [ arg3>arg2 && 0==arg1 ], cost: arg3-arg2 15: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, arg3'=arg1, [ 1==arg3 ], cost: 1 16: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=1, arg2'=1+arg2, arg3'=arg1, [ 0==arg3 ], cost: 1 17: __init -> f1_0_main_Load : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f1549_0_search_LT -> f1911_0_search_GE : arg2'=0, arg3'=arg3P_2, [], cost: 1 5: f1549_0_search_LT -> f1944_0_displayChessboard_GE : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 24: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [], cost: NONTERM 25: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [ arg1>-1 ], cost: NONTERM 3: f1911_0_search_GE -> f1549_0_search_LT : arg1'=1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 1 11: f1911_0_search_GE -> f1876_0_safeMove_GE : arg1'=1, arg2'=0, arg3'=arg1, [], cost: 1 6: f1944_0_displayChessboard_GE -> f2167_0_displayChessboard_GE : arg2'=0, arg3'=arg3P_7, [], cost: 1 26: f1944_0_displayChessboard_GE -> [9] : arg2'=0, arg3'=arg3P_7, [], cost: NONTERM 7: f2167_0_displayChessboard_GE -> f1944_0_displayChessboard_GE : arg1'=1+arg1, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 12: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=1, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 13: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=0, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 15: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, arg3'=arg1, [ 1==arg3 ], cost: 1 16: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=1, arg2'=1+arg2, arg3'=arg1, [ 0==arg3 ], cost: 1 27: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg1, arg3'=arg1, [ 1==arg3 && arg1>1+arg2 ], cost: arg1-arg2 17: __init -> f1_0_main_Load : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 1: f1549_0_search_LT -> f1911_0_search_GE : arg2'=0, arg3'=arg3P_2, [], cost: 1 5: f1549_0_search_LT -> f1944_0_displayChessboard_GE : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 24: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [], cost: NONTERM 25: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [ arg1>-1 ], cost: NONTERM 3: f1911_0_search_GE -> f1549_0_search_LT : arg1'=1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 1 11: f1911_0_search_GE -> f1876_0_safeMove_GE : arg1'=1, arg2'=0, arg3'=arg1, [], cost: 1 26: f1944_0_displayChessboard_GE -> [9] : arg2'=0, arg3'=arg3P_7, [], cost: NONTERM 29: f1944_0_displayChessboard_GE -> f1944_0_displayChessboard_GE : arg1'=1+arg1, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 2 12: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=1, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 13: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=0, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 15: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, arg3'=arg1, [ 1==arg3 ], cost: 1 16: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=1, arg2'=1+arg2, arg3'=arg1, [ 0==arg3 ], cost: 1 27: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg1, arg3'=arg1, [ 1==arg3 && arg1>1+arg2 ], cost: arg1-arg2 28: __init -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_18>0 && arg2P_18>-1 ], cost: 2 Accelerating simple loops of location 3. Accelerating the following rules: 29: f1944_0_displayChessboard_GE -> f1944_0_displayChessboard_GE : arg1'=1+arg1, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 2 Accelerated rule 29 with NONTERM, yielding the new rule 30. Removing the simple loops: 29. Accelerated all simple loops using metering functions (where possible): Start location: __init 1: f1549_0_search_LT -> f1911_0_search_GE : arg2'=0, arg3'=arg3P_2, [], cost: 1 5: f1549_0_search_LT -> f1944_0_displayChessboard_GE : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 24: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [], cost: NONTERM 25: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [ arg1>-1 ], cost: NONTERM 3: f1911_0_search_GE -> f1549_0_search_LT : arg1'=1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 1 11: f1911_0_search_GE -> f1876_0_safeMove_GE : arg1'=1, arg2'=0, arg3'=arg1, [], cost: 1 26: f1944_0_displayChessboard_GE -> [9] : arg2'=0, arg3'=arg3P_7, [], cost: NONTERM 30: f1944_0_displayChessboard_GE -> [11] : [], cost: NONTERM 12: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=1, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 13: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=0, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 15: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, arg3'=arg1, [ 1==arg3 ], cost: 1 16: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=1, arg2'=1+arg2, arg3'=arg1, [ 0==arg3 ], cost: 1 27: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg1, arg3'=arg1, [ 1==arg3 && arg1>1+arg2 ], cost: arg1-arg2 28: __init -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_18>0 && arg2P_18>-1 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 1: f1549_0_search_LT -> f1911_0_search_GE : arg2'=0, arg3'=arg3P_2, [], cost: 1 5: f1549_0_search_LT -> f1944_0_displayChessboard_GE : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 24: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [], cost: NONTERM 25: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [ arg1>-1 ], cost: NONTERM 31: f1549_0_search_LT -> [11] : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: NONTERM 3: f1911_0_search_GE -> f1549_0_search_LT : arg1'=1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 1 11: f1911_0_search_GE -> f1876_0_safeMove_GE : arg1'=1, arg2'=0, arg3'=arg1, [], cost: 1 26: f1944_0_displayChessboard_GE -> [9] : arg2'=0, arg3'=arg3P_7, [], cost: NONTERM 12: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=1, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 13: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=0, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 15: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, arg3'=arg1, [ 1==arg3 ], cost: 1 16: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=1, arg2'=1+arg2, arg3'=arg1, [ 0==arg3 ], cost: 1 27: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg1, arg3'=arg1, [ 1==arg3 && arg1>1+arg2 ], cost: arg1-arg2 28: __init -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_18>0 && arg2P_18>-1 ], cost: 2 Eliminated locations (on linear paths): Start location: __init 1: f1549_0_search_LT -> f1911_0_search_GE : arg2'=0, arg3'=arg3P_2, [], cost: 1 24: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [], cost: NONTERM 25: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [ arg1>-1 ], cost: NONTERM 31: f1549_0_search_LT -> [11] : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: NONTERM 32: f1549_0_search_LT -> [9] : arg1'=0, arg2'=0, arg3'=arg3P_7, [], cost: NONTERM 3: f1911_0_search_GE -> f1549_0_search_LT : arg1'=1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 1 11: f1911_0_search_GE -> f1876_0_safeMove_GE : arg1'=1, arg2'=0, arg3'=arg1, [], cost: 1 12: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=1, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 13: f1876_0_safeMove_GE -> f1969_0_safeMove_NE : arg1'=arg3, arg3'=0, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 1 15: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, arg3'=arg1, [ 1==arg3 ], cost: 1 16: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=1, arg2'=1+arg2, arg3'=arg1, [ 0==arg3 ], cost: 1 27: f1969_0_safeMove_NE -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg1, arg3'=arg1, [ 1==arg3 && arg1>1+arg2 ], cost: arg1-arg2 28: __init -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_18>0 && arg2P_18>-1 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 24: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [], cost: NONTERM 25: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [ arg1>-1 ], cost: NONTERM 31: f1549_0_search_LT -> [11] : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: NONTERM 32: f1549_0_search_LT -> [9] : arg1'=0, arg2'=0, arg3'=arg3P_7, [], cost: NONTERM 33: f1549_0_search_LT -> f1549_0_search_LT : arg1'=1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 2 34: f1549_0_search_LT -> f1876_0_safeMove_GE : arg1'=1, arg2'=0, arg3'=arg1, [], cost: 2 35: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, arg3'=arg3, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 2 36: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg3, arg3'=arg3, [ arg3>0 && arg1>0 && arg3>1+arg2 ], cost: 1+arg3-arg2 37: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=1, arg2'=1+arg2, arg3'=arg3, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 2 28: __init -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_18>0 && arg2P_18>-1 ], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 33: f1549_0_search_LT -> f1549_0_search_LT : arg1'=1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 2 Accelerated rule 33 with NONTERM, yielding the new rule 38. Removing the simple loops: 33. Accelerating simple loops of location 5. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 35: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 2 36: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg3, [ arg3>0 && arg1>0 && arg3>1+arg2 ], cost: 1+arg3-arg2 37: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=1, arg2'=1+arg2, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 2 Found no metering function for rule 35. Found no metering function for rule 36. Accelerated rule 37 with metering function arg3-arg2, yielding the new rule 39. Removing the simple loops: 37. Accelerated all simple loops using metering functions (where possible): Start location: __init 24: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [], cost: NONTERM 25: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [ arg1>-1 ], cost: NONTERM 31: f1549_0_search_LT -> [11] : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: NONTERM 32: f1549_0_search_LT -> [9] : arg1'=0, arg2'=0, arg3'=arg3P_7, [], cost: NONTERM 34: f1549_0_search_LT -> f1876_0_safeMove_GE : arg1'=1, arg2'=0, arg3'=arg1, [], cost: 2 38: f1549_0_search_LT -> [12] : [ arg1>-1 ], cost: NONTERM 35: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=0, arg2'=1+arg2, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 2 36: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg3, [ arg3>0 && arg1>0 && arg3>1+arg2 ], cost: 1+arg3-arg2 39: f1876_0_safeMove_GE -> f1876_0_safeMove_GE : arg1'=1, arg2'=arg3, [ arg3>0 && arg1>0 && arg3>arg2 ], cost: 2*arg3-2*arg2 28: __init -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_18>0 && arg2P_18>-1 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 24: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [], cost: NONTERM 25: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [ arg1>-1 ], cost: NONTERM 31: f1549_0_search_LT -> [11] : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: NONTERM 32: f1549_0_search_LT -> [9] : arg1'=0, arg2'=0, arg3'=arg3P_7, [], cost: NONTERM 34: f1549_0_search_LT -> f1876_0_safeMove_GE : arg1'=1, arg2'=0, arg3'=arg1, [], cost: 2 41: f1549_0_search_LT -> f1876_0_safeMove_GE : arg1'=0, arg2'=1, arg3'=arg1, [ arg1>0 ], cost: 4 42: f1549_0_search_LT -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg1, arg3'=arg1, [ arg1>1 ], cost: 3+arg1 43: f1549_0_search_LT -> f1876_0_safeMove_GE : arg1'=1, arg2'=arg1, arg3'=arg1, [ arg1>0 ], cost: 2+2*arg1 28: __init -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_18>0 && arg2P_18>-1 ], cost: 2 40: __init -> [12] : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: __init 24: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [], cost: NONTERM 25: f1549_0_search_LT -> [8] : arg2'=0, arg3'=arg3P_2, [ arg1>-1 ], cost: NONTERM 31: f1549_0_search_LT -> [11] : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: NONTERM 32: f1549_0_search_LT -> [9] : arg1'=0, arg2'=0, arg3'=arg3P_7, [], cost: NONTERM 42: f1549_0_search_LT -> f1876_0_safeMove_GE : arg1'=0, arg2'=arg1, arg3'=arg1, [ arg1>1 ], cost: 3+arg1 43: f1549_0_search_LT -> f1876_0_safeMove_GE : arg1'=1, arg2'=arg1, arg3'=arg1, [ arg1>0 ], cost: 2+2*arg1 28: __init -> f1549_0_search_LT : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_18>0 && arg2P_18>-1 ], cost: 2 40: __init -> [12] : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: __init 40: __init -> [12] : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [], cost: NONTERM 44: __init -> [8] : arg1'=0, arg2'=0, arg3'=arg3P_2, [ arg1P_18>0 && arg2P_18>-1 ], cost: NONTERM 45: __init -> [8] : arg1'=0, arg2'=0, arg3'=arg3P_2, [ arg1P_18>0 && arg2P_18>-1 ], cost: NONTERM 46: __init -> [11] : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1P_18>0 && arg2P_18>-1 ], cost: NONTERM 47: __init -> [9] : arg1'=0, arg2'=0, arg3'=arg3P_7, [ arg1P_18>0 && arg2P_18>-1 ], cost: NONTERM Applied pruning (of leafs and parallel rules): Start location: __init 40: __init -> [12] : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [], cost: NONTERM 45: __init -> [8] : arg1'=0, arg2'=0, arg3'=arg3P_2, [ arg1P_18>0 && arg2P_18>-1 ], cost: NONTERM 46: __init -> [11] : arg1'=0, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1P_18>0 && arg2P_18>-1 ], cost: NONTERM 47: __init -> [9] : arg1'=0, arg2'=0, arg3'=arg3P_7, [ arg1P_18>0 && arg2P_18>-1 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 40: __init -> [12] : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_1, [], cost: NONTERM 47: __init -> [9] : arg1'=0, arg2'=0, arg3'=arg3P_7, [ arg1P_18>0 && arg2P_18>-1 ], cost: NONTERM Computing asymptotic complexity for rule 40 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [] NO