WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, [ 0==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 && arg5==arg5P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1==arg1P_2 && 1==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 && arg5==arg5P_2 ], cost: 1 2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg4==arg4P_3 && arg5==arg5P_3 ], cost: 1 3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && arg5==arg5P_4 ], cost: 1 4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 19: f6 -> f7 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, arg5'=arg5P_20, [ arg40 && arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 && arg5==arg5P_20 ], cost: 1 21: f6 -> f18 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, arg5'=arg5P_22, [ arg4>=arg5 && arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 && arg5==arg5P_22 ], cost: 1 22: f6 -> f18 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, arg5'=arg5P_23, [ arg2<=0 && arg1==arg1P_23 && arg2==arg2P_23 && arg3==arg3P_23 && arg4==arg4P_23 && arg5==arg5P_23 ], cost: 1 5: f8 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg4P_6==arg3*arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg5==arg5P_6 ], cost: 1 16: f11 -> f10 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, arg5'=arg5P_17, [ arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 && arg5==arg5P_17 ], cost: 1 6: f12 -> f15 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg4P_7==-arg3*arg4 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg5==arg5P_7 ], cost: 1 11: f15 -> f14 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 && arg5==arg5P_12 ], cost: 1 7: f13 -> f16 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg1==arg1P_8 && 0==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 && arg5==arg5P_8 ], cost: 1 12: f16 -> f14 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 && arg5==arg5P_13 ], cost: 1 8: f9 -> f12 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [ arg4>0 && arg3<-1 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 && arg5==arg5P_9 ], cost: 1 9: f9 -> f13 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, [ arg4<=0 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 && arg5==arg5P_10 ], cost: 1 10: f9 -> f13 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, [ arg3>=-1 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 && arg5==arg5P_11 ], cost: 1 17: f14 -> f10 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, arg5'=arg5P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 && arg5==arg5P_18 ], cost: 1 13: f7 -> f8 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, arg5'=arg5P_14, [ arg4>0 && arg3>1 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 && arg5==arg5P_14 ], cost: 1 14: f7 -> f9 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, [ arg4<=0 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 && arg5==arg5P_15 ], cost: 1 15: f7 -> f9 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, arg5'=arg5P_16, [ arg3<=1 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 && arg4==arg4P_16 && arg5==arg5P_16 ], cost: 1 18: f10 -> f17 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, arg5'=arg5P_19, [ arg1P_19==1+arg1 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 && arg5==arg5P_19 ], cost: 1 20: f17 -> f6 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, arg5'=arg5P_21, [ arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 && arg4==arg4P_21 && arg5==arg5P_21 ], cost: 1 23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, arg5'=arg5P_24, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, arg5'=arg5P_24, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, [ 0==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 && arg5==arg5P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1==arg1P_2 && 1==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 && arg5==arg5P_2 ], cost: 1 2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg4==arg4P_3 && arg5==arg5P_3 ], cost: 1 3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && arg5==arg5P_4 ], cost: 1 4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 19: f6 -> f7 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, arg5'=arg5P_20, [ arg40 && arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 && arg5==arg5P_20 ], cost: 1 5: f8 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg4P_6==arg3*arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg5==arg5P_6 ], cost: 1 16: f11 -> f10 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, arg5'=arg5P_17, [ arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 && arg5==arg5P_17 ], cost: 1 6: f12 -> f15 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg4P_7==-arg3*arg4 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg5==arg5P_7 ], cost: 1 11: f15 -> f14 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 && arg5==arg5P_12 ], cost: 1 7: f13 -> f16 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg1==arg1P_8 && 0==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 && arg5==arg5P_8 ], cost: 1 12: f16 -> f14 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 && arg5==arg5P_13 ], cost: 1 8: f9 -> f12 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [ arg4>0 && arg3<-1 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 && arg5==arg5P_9 ], cost: 1 9: f9 -> f13 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, [ arg4<=0 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 && arg5==arg5P_10 ], cost: 1 10: f9 -> f13 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, [ arg3>=-1 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 && arg5==arg5P_11 ], cost: 1 17: f14 -> f10 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, arg5'=arg5P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 && arg5==arg5P_18 ], cost: 1 13: f7 -> f8 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, arg5'=arg5P_14, [ arg4>0 && arg3>1 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 && arg5==arg5P_14 ], cost: 1 14: f7 -> f9 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, [ arg4<=0 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 && arg5==arg5P_15 ], cost: 1 15: f7 -> f9 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, arg5'=arg5P_16, [ arg3<=1 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 && arg4==arg4P_16 && arg5==arg5P_16 ], cost: 1 18: f10 -> f17 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, arg5'=arg5P_19, [ arg1P_19==1+arg1 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 && arg5==arg5P_19 ], cost: 1 20: f17 -> f6 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, arg5'=arg5P_21, [ arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 && arg4==arg4P_21 && arg5==arg5P_21 ], cost: 1 23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, arg5'=arg5P_24, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=0, [], cost: 1 1: f2 -> f3 : arg2'=1, [], cost: 1 2: f3 -> f4 : arg3'=arg3P_3, [], cost: 1 3: f4 -> f5 : arg4'=arg4P_4, [], cost: 1 4: f5 -> f6 : arg5'=arg5P_5, [], cost: 1 19: f6 -> f7 : [ arg40 ], cost: 1 5: f8 -> f11 : arg4'=arg3*arg4, [], cost: 1 16: f11 -> f10 : [], cost: 1 6: f12 -> f15 : arg4'=-arg3*arg4, [], cost: 1 11: f15 -> f14 : [], cost: 1 7: f13 -> f16 : arg2'=0, [], cost: 1 12: f16 -> f14 : [], cost: 1 8: f9 -> f12 : [ arg4>0 && arg3<-1 ], cost: 1 9: f9 -> f13 : [ arg4<=0 ], cost: 1 10: f9 -> f13 : [ arg3>=-1 ], cost: 1 17: f14 -> f10 : [], cost: 1 13: f7 -> f8 : [ arg4>0 && arg3>1 ], cost: 1 14: f7 -> f9 : [ arg4<=0 ], cost: 1 15: f7 -> f9 : [ arg3<=1 ], cost: 1 18: f10 -> f17 : arg1'=1+arg1, [], cost: 1 20: f17 -> f6 : [], cost: 1 23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, arg5'=arg5P_24, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 19: f6 -> f7 : [ arg40 ], cost: 1 33: f13 -> f14 : arg2'=0, [], cost: 2 9: f9 -> f13 : [ arg4<=0 ], cost: 1 10: f9 -> f13 : [ arg3>=-1 ], cost: 1 32: f9 -> f14 : arg4'=-arg3*arg4, [ arg4>0 && arg3<-1 ], cost: 3 17: f14 -> f10 : [], cost: 1 14: f7 -> f9 : [ arg4<=0 ], cost: 1 15: f7 -> f9 : [ arg3<=1 ], cost: 1 30: f7 -> f10 : arg4'=arg3*arg4, [ arg4>0 && arg3>1 ], cost: 3 34: f10 -> f6 : arg1'=1+arg1, [], cost: 2 28: __init -> f6 : arg1'=0, arg2'=1, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [], cost: 6 Eliminated locations (on tree-shaped paths): Start location: __init 35: f6 -> f9 : [ arg40 && arg4<=0 ], cost: 2 36: f6 -> f9 : [ arg40 && arg3<=1 ], cost: 2 37: f6 -> f10 : arg4'=arg3*arg4, [ arg40 && arg4>0 && arg3>1 ], cost: 4 40: f9 -> f10 : arg4'=-arg3*arg4, [ arg4>0 && arg3<-1 ], cost: 4 41: f9 -> f10 : arg2'=0, [ arg4<=0 ], cost: 4 42: f9 -> f10 : arg2'=0, [ arg3>=-1 ], cost: 4 34: f10 -> f6 : arg1'=1+arg1, [], cost: 2 28: __init -> f6 : arg1'=0, arg2'=1, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [], cost: 6 Eliminated locations (on tree-shaped paths): Start location: __init 48: f6 -> f6 : arg1'=1+arg1, arg4'=arg3*arg4, [ arg40 && arg4>0 && arg3>1 ], cost: 6 49: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg4<=0 ], cost: 8 50: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg4<=0 && arg3>=-1 ], cost: 8 51: f6 -> f6 : arg1'=1+arg1, arg4'=-arg3*arg4, [ arg40 && arg4>0 && arg3<-1 ], cost: 8 52: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg3<=1 && arg4<=0 ], cost: 8 53: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg3<=1 && arg3>=-1 ], cost: 8 28: __init -> f6 : arg1'=0, arg2'=1, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [], cost: 6 Accelerating simple loops of location 5. Accelerating the following rules: 48: f6 -> f6 : arg1'=1+arg1, arg4'=arg3*arg4, [ arg40 && arg4>0 && arg3>1 ], cost: 6 49: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg4<=0 ], cost: 8 50: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg4<=0 && arg3>=-1 ], cost: 8 51: f6 -> f6 : arg1'=1+arg1, arg4'=-arg3*arg4, [ arg40 && arg4>0 && arg3<-1 ], cost: 8 52: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg3<=1 && arg4<=0 ], cost: 8 53: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg3<=1 && arg3>=-1 ], cost: 8 Accelerated rule 48 with backward acceleration, yielding the new rule 54. Failed to prove monotonicity of the guard of rule 49. Failed to prove monotonicity of the guard of rule 50. Accelerated rule 51 with backward acceleration, yielding the new rule 55. Failed to prove monotonicity of the guard of rule 52. Failed to prove monotonicity of the guard of rule 53. [accelerate] Nesting with 6 inner and 6 outer candidates Removing the simple loops: 48 51. Accelerated all simple loops using metering functions (where possible): Start location: __init 49: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg4<=0 ], cost: 8 50: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg4<=0 && arg3>=-1 ], cost: 8 52: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg3<=1 && arg4<=0 ], cost: 8 53: f6 -> f6 : arg1'=1+arg1, arg2'=0, [ arg40 && arg3<=1 && arg3>=-1 ], cost: 8 54: f6 -> f6 : arg1'=arg1+k, arg4'=arg3^k*arg4, [ arg2>0 && arg4>0 && arg3>1 && k>=0 && arg4*arg3^(-1+k) f6 : arg1'=k_3+arg1, arg4'=(-arg3)^k_3*arg4, [ arg2>0 && arg4>0 && arg3<-1 && k_3>=0 && (-arg3)^(-1+k_3)*arg4 f6 : arg1'=0, arg2'=1, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [], cost: 6 Chained accelerated rules (with incoming rules): Start location: __init 28: __init -> f6 : arg1'=0, arg2'=1, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [], cost: 6 56: __init -> f6 : arg1'=1, arg2'=0, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [ arg4P_4 f6 : arg1'=1, arg2'=0, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [ arg4P_4=-1 ], cost: 14 58: __init -> f6 : arg1'=1, arg2'=0, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [ arg4P_4 f6 : arg1'=1, arg2'=0, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [ arg4P_4=-1 ], cost: 14 60: __init -> f6 : arg1'=k, arg2'=1, arg3'=arg3P_3, arg4'=arg3P_3^k*arg4P_4, arg5'=arg5P_5, [ arg4P_4>0 && arg3P_3>1 && k>=0 && arg3P_3^(-1+k)*arg4P_4 f6 : arg1'=k_3, arg2'=1, arg3'=arg3P_3, arg4'=(-arg3P_3)^k_3*arg4P_4, arg5'=arg5P_5, [ arg4P_4>0 && arg3P_3<-1 && k_3>=0 && (-arg3P_3)^(-1+k_3)*arg4P_4 f6 : arg1'=k, arg2'=1, arg3'=arg3P_3, arg4'=arg3P_3^k*arg4P_4, arg5'=arg5P_5, [ arg4P_4>0 && arg3P_3>1 && k>=0 && arg3P_3^(-1+k)*arg4P_4 f6 : arg1'=k_3, arg2'=1, arg3'=arg3P_3, arg4'=(-arg3P_3)^k_3*arg4P_4, arg5'=arg5P_5, [ arg4P_4>0 && arg3P_3<-1 && k_3>=0 && (-arg3P_3)^(-1+k_3)*arg4P_4 f6 : arg1'=k, arg2'=1, arg3'=arg3P_3, arg4'=arg3P_3^k*arg4P_4, arg5'=arg5P_5, [ arg4P_4>0 && arg3P_3>1 && k>=0 && arg3P_3^(-1+k)*arg4P_4 f6 : arg1'=k_3, arg2'=1, arg3'=arg3P_3, arg4'=(-arg3P_3)^k_3*arg4P_4, arg5'=arg5P_5, [ arg4P_4>0 && arg3P_3<-1 && k_3>=0 && (-arg3P_3)^(-1+k_3)*arg4P_4