WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l6 0: l0 -> l2 : delta^0'=delta^post_1, delta_new^0'=delta_new^post_1, deltaext^0'=deltaext^post_1, deltaext_new^0'=deltaext_new^post_1, deltext^0'=deltext^post_1, wnt^0'=wnt^post_1, wntext^0'=wntext^post_1, [ 1+delta^0<=delta_new^0 && delta^0==delta^post_1 && delta_new^0==delta_new^post_1 && deltaext^0==deltaext^post_1 && deltaext_new^0==deltaext_new^post_1 && deltext^0==deltext^post_1 && wnt^0==wnt^post_1 && wntext^0==wntext^post_1 ], cost: 1 1: l0 -> l2 : delta^0'=delta^post_2, delta_new^0'=delta_new^post_2, deltaext^0'=deltaext^post_2, deltaext_new^0'=deltaext_new^post_2, deltext^0'=deltext^post_2, wnt^0'=wnt^post_2, wntext^0'=wntext^post_2, [ 1+delta_new^0<=delta^0 && delta^0==delta^post_2 && delta_new^0==delta_new^post_2 && deltaext^0==deltaext^post_2 && deltaext_new^0==deltaext_new^post_2 && deltext^0==deltext^post_2 && wnt^0==wnt^post_2 && wntext^0==wntext^post_2 ], cost: 1 3: l0 -> l3 : delta^0'=delta^post_4, delta_new^0'=delta_new^post_4, deltaext^0'=deltaext^post_4, deltaext_new^0'=deltaext_new^post_4, deltext^0'=deltext^post_4, wnt^0'=wnt^post_4, wntext^0'=wntext^post_4, [ 1+deltaext^0<=deltaext_new^0 && delta^0==delta^post_4 && delta_new^0==delta_new^post_4 && deltaext^0==deltaext^post_4 && deltaext_new^0==deltaext_new^post_4 && deltext^0==deltext^post_4 && wnt^0==wnt^post_4 && wntext^0==wntext^post_4 ], cost: 1 4: l0 -> l3 : delta^0'=delta^post_5, delta_new^0'=delta_new^post_5, deltaext^0'=deltaext^post_5, deltaext_new^0'=deltaext_new^post_5, deltext^0'=deltext^post_5, wnt^0'=wnt^post_5, wntext^0'=wntext^post_5, [ 1+deltaext_new^0<=deltaext^0 && delta^0==delta^post_5 && delta_new^0==delta_new^post_5 && deltaext^0==deltaext^post_5 && deltaext_new^0==deltaext_new^post_5 && deltext^0==deltext^post_5 && wnt^0==wnt^post_5 && wntext^0==wntext^post_5 ], cost: 1 2: l2 -> l1 : delta^0'=delta^post_3, delta_new^0'=delta_new^post_3, deltaext^0'=deltaext^post_3, deltaext_new^0'=deltaext_new^post_3, deltext^0'=deltext^post_3, wnt^0'=wnt^post_3, wntext^0'=wntext^post_3, [ deltaext^post_3==deltaext_new^0 && delta^post_3==delta_new^0 && delta_new^0==delta_new^post_3 && deltaext_new^0==deltaext_new^post_3 && deltext^0==deltext^post_3 && wnt^0==wnt^post_3 && wntext^0==wntext^post_3 ], cost: 1 10: l1 -> l4 : delta^0'=delta^post_11, delta_new^0'=delta_new^post_11, deltaext^0'=deltaext^post_11, deltaext_new^0'=deltaext_new^post_11, deltext^0'=deltext^post_11, wnt^0'=wnt^post_11, wntext^0'=wntext^post_11, [ 2+wnt^0<=-1+2*deltaext^0 && -1+2*deltaext^0<=2+wnt^0 && deltaext_new^post_11==deltaext^0 && delta^0==delta^post_11 && delta_new^0==delta_new^post_11 && deltaext^0==deltaext^post_11 && deltext^0==deltext^post_11 && wnt^0==wnt^post_11 && wntext^0==wntext^post_11 ], cost: 1 11: l1 -> l4 : delta^0'=delta^post_12, delta_new^0'=delta_new^post_12, deltaext^0'=deltaext^post_12, deltaext_new^0'=deltaext_new^post_12, deltext^0'=deltext^post_12, wnt^0'=wnt^post_12, wntext^0'=wntext^post_12, [ 2+wnt^0<=2*deltaext^0 && 2*deltaext^0<=2+wnt^0 && deltaext_new^post_12==deltaext^0 && delta^0==delta^post_12 && delta_new^0==delta_new^post_12 && deltaext^0==deltaext^post_12 && deltext^0==deltext^post_12 && wnt^0==wnt^post_12 && wntext^0==wntext^post_12 ], cost: 1 12: l1 -> l4 : delta^0'=delta^post_13, delta_new^0'=delta_new^post_13, deltaext^0'=deltaext^post_13, deltaext_new^0'=deltaext_new^post_13, deltext^0'=deltext^post_13, wnt^0'=wnt^post_13, wntext^0'=wntext^post_13, [ 3+wnt^0<=-1+2*deltaext^0 && deltaext_new^post_13==-1+deltaext^0 && delta^0==delta^post_13 && delta_new^0==delta_new^post_13 && deltaext^0==deltaext^post_13 && deltext^0==deltext^post_13 && wnt^0==wnt^post_13 && wntext^0==wntext^post_13 ], cost: 1 13: l1 -> l4 : delta^0'=delta^post_14, delta_new^0'=delta_new^post_14, deltaext^0'=deltaext^post_14, deltaext_new^0'=deltaext_new^post_14, deltext^0'=deltext^post_14, wnt^0'=wnt^post_14, wntext^0'=wntext^post_14, [ 1+2*deltaext^0<=2+wnt^0 && deltaext_new^post_14==1+deltaext^0 && delta^0==delta^post_14 && delta_new^0==delta_new^post_14 && deltaext^0==deltaext^post_14 && deltext^0==deltext^post_14 && wnt^0==wnt^post_14 && wntext^0==wntext^post_14 ], cost: 1 5: l3 -> l1 : delta^0'=delta^post_6, delta_new^0'=delta_new^post_6, deltaext^0'=deltaext^post_6, deltaext_new^0'=deltaext_new^post_6, deltext^0'=deltext^post_6, wnt^0'=wnt^post_6, wntext^0'=wntext^post_6, [ deltaext^post_6==deltaext_new^0 && delta^post_6==delta_new^0 && delta_new^0==delta_new^post_6 && deltaext_new^0==deltaext_new^post_6 && deltext^0==deltext^post_6 && wnt^0==wnt^post_6 && wntext^0==wntext^post_6 ], cost: 1 6: l4 -> l0 : delta^0'=delta^post_7, delta_new^0'=delta_new^post_7, deltaext^0'=deltaext^post_7, deltaext_new^0'=deltaext_new^post_7, deltext^0'=deltext^post_7, wnt^0'=wnt^post_7, wntext^0'=wntext^post_7, [ deltaext^0+wntext^0<=-1+2*delta^0 && -1+2*delta^0<=deltaext^0+wntext^0 && delta_new^post_7==delta^0 && delta^0==delta^post_7 && deltaext^0==deltaext^post_7 && deltaext_new^0==deltaext_new^post_7 && deltext^0==deltext^post_7 && wnt^0==wnt^post_7 && wntext^0==wntext^post_7 ], cost: 1 7: l4 -> l0 : delta^0'=delta^post_8, delta_new^0'=delta_new^post_8, deltaext^0'=deltaext^post_8, deltaext_new^0'=deltaext_new^post_8, deltext^0'=deltext^post_8, wnt^0'=wnt^post_8, wntext^0'=wntext^post_8, [ deltaext^0+wntext^0<=2*delta^0 && 2*delta^0<=deltaext^0+wntext^0 && delta_new^post_8==delta^0 && delta^0==delta^post_8 && deltaext^0==deltaext^post_8 && deltaext_new^0==deltaext_new^post_8 && deltext^0==deltext^post_8 && wnt^0==wnt^post_8 && wntext^0==wntext^post_8 ], cost: 1 8: l4 -> l0 : delta^0'=delta^post_9, delta_new^0'=delta_new^post_9, deltaext^0'=deltaext^post_9, deltaext_new^0'=deltaext_new^post_9, deltext^0'=deltext^post_9, wnt^0'=wnt^post_9, wntext^0'=wntext^post_9, [ 1+deltaext^0+wntext^0<=-1+2*delta^0 && delta_new^post_9==-1+delta^0 && delta^0==delta^post_9 && deltaext^0==deltaext^post_9 && deltaext_new^0==deltaext_new^post_9 && deltext^0==deltext^post_9 && wnt^0==wnt^post_9 && wntext^0==wntext^post_9 ], cost: 1 9: l4 -> l0 : delta^0'=delta^post_10, delta_new^0'=delta_new^post_10, deltaext^0'=deltaext^post_10, deltaext_new^0'=deltaext_new^post_10, deltext^0'=deltext^post_10, wnt^0'=wnt^post_10, wntext^0'=wntext^post_10, [ 1+2*delta^0<=deltaext^0+wntext^0 && delta_new^post_10==1+delta^0 && delta^0==delta^post_10 && deltaext^0==deltaext^post_10 && deltaext_new^0==deltaext_new^post_10 && deltext^0==deltext^post_10 && wnt^0==wnt^post_10 && wntext^0==wntext^post_10 ], cost: 1 14: l5 -> l1 : delta^0'=delta^post_15, delta_new^0'=delta_new^post_15, deltaext^0'=deltaext^post_15, deltaext_new^0'=deltaext_new^post_15, deltext^0'=deltext^post_15, wnt^0'=wnt^post_15, wntext^0'=wntext^post_15, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && delta^0==delta^post_15 && delta_new^0==delta_new^post_15 && deltaext^0==deltaext^post_15 && deltaext_new^0==deltaext_new^post_15 && deltext^0==deltext^post_15 && wnt^0==wnt^post_15 && wntext^0==wntext^post_15 ], cost: 1 15: l6 -> l5 : delta^0'=delta^post_16, delta_new^0'=delta_new^post_16, deltaext^0'=deltaext^post_16, deltaext_new^0'=deltaext_new^post_16, deltext^0'=deltext^post_16, wnt^0'=wnt^post_16, wntext^0'=wntext^post_16, [ delta^0==delta^post_16 && delta_new^0==delta_new^post_16 && deltaext^0==deltaext^post_16 && deltaext_new^0==deltaext_new^post_16 && deltext^0==deltext^post_16 && wnt^0==wnt^post_16 && wntext^0==wntext^post_16 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 15: l6 -> l5 : delta^0'=delta^post_16, delta_new^0'=delta_new^post_16, deltaext^0'=deltaext^post_16, deltaext_new^0'=deltaext_new^post_16, deltext^0'=deltext^post_16, wnt^0'=wnt^post_16, wntext^0'=wntext^post_16, [ delta^0==delta^post_16 && delta_new^0==delta_new^post_16 && deltaext^0==deltaext^post_16 && deltaext_new^0==deltaext_new^post_16 && deltext^0==deltext^post_16 && wnt^0==wnt^post_16 && wntext^0==wntext^post_16 ], cost: 1 Simplified all rules, resulting in: Start location: l6 0: l0 -> l2 : [ 1+delta^0<=delta_new^0 ], cost: 1 1: l0 -> l2 : [ 1+delta_new^0<=delta^0 ], cost: 1 3: l0 -> l3 : [ 1+deltaext^0<=deltaext_new^0 ], cost: 1 4: l0 -> l3 : [ 1+deltaext_new^0<=deltaext^0 ], cost: 1 2: l2 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [], cost: 1 10: l1 -> l4 : deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 ], cost: 1 11: l1 -> l4 : deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 ], cost: 1 12: l1 -> l4 : deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 ], cost: 1 13: l1 -> l4 : deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 ], cost: 1 5: l3 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [], cost: 1 6: l4 -> l0 : delta_new^0'=delta^0, [ 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 1 7: l4 -> l0 : delta_new^0'=delta^0, [ deltaext^0+wntext^0-2*delta^0==0 ], cost: 1 8: l4 -> l0 : delta_new^0'=-1+delta^0, [ 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 1 9: l4 -> l0 : delta_new^0'=1+delta^0, [ 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 1 14: l5 -> l1 : [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 ], cost: 1 15: l6 -> l5 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l6 0: l0 -> l2 : [ 1+delta^0<=delta_new^0 ], cost: 1 1: l0 -> l2 : [ 1+delta_new^0<=delta^0 ], cost: 1 3: l0 -> l3 : [ 1+deltaext^0<=deltaext_new^0 ], cost: 1 4: l0 -> l3 : [ 1+deltaext_new^0<=deltaext^0 ], cost: 1 2: l2 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [], cost: 1 10: l1 -> l4 : deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 ], cost: 1 11: l1 -> l4 : deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 ], cost: 1 12: l1 -> l4 : deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 ], cost: 1 13: l1 -> l4 : deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 ], cost: 1 5: l3 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [], cost: 1 6: l4 -> l0 : delta_new^0'=delta^0, [ 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 1 7: l4 -> l0 : delta_new^0'=delta^0, [ deltaext^0+wntext^0-2*delta^0==0 ], cost: 1 8: l4 -> l0 : delta_new^0'=-1+delta^0, [ 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 1 9: l4 -> l0 : delta_new^0'=1+delta^0, [ 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 1 16: l6 -> l1 : [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l6 33: l0 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [ 1+delta^0<=delta_new^0 ], cost: 2 34: l0 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [ 1+delta_new^0<=delta^0 ], cost: 2 35: l0 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [ 1+deltaext^0<=deltaext_new^0 ], cost: 2 36: l0 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [ 1+deltaext_new^0<=deltaext^0 ], cost: 2 17: l1 -> l0 : delta_new^0'=delta^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 2 18: l1 -> l0 : delta_new^0'=delta^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 2 19: l1 -> l0 : delta_new^0'=-1+delta^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 2 20: l1 -> l0 : delta_new^0'=1+delta^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 2 21: l1 -> l0 : delta_new^0'=delta^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 2 22: l1 -> l0 : delta_new^0'=delta^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 2 23: l1 -> l0 : delta_new^0'=-1+delta^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 2 24: l1 -> l0 : delta_new^0'=1+delta^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 2 25: l1 -> l0 : delta_new^0'=delta^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 2 26: l1 -> l0 : delta_new^0'=delta^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 2 27: l1 -> l0 : delta_new^0'=-1+delta^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 2 28: l1 -> l0 : delta_new^0'=1+delta^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 2 29: l1 -> l0 : delta_new^0'=delta^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 2 30: l1 -> l0 : delta_new^0'=delta^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 2 31: l1 -> l0 : delta_new^0'=-1+delta^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 2 32: l1 -> l0 : delta_new^0'=1+delta^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 2 16: l6 -> l1 : [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l6 37: l1 -> l1 : delta^0'=-1+delta^0, delta_new^0'=-1+delta^0, deltaext^0'=deltaext^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 4 38: l1 -> l1 : delta^0'=1+delta^0, delta_new^0'=1+delta^0, deltaext^0'=deltaext^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 39: l1 -> l1 : delta^0'=-1+delta^0, delta_new^0'=-1+delta^0, deltaext^0'=deltaext^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 4 40: l1 -> l1 : delta^0'=1+delta^0, delta_new^0'=1+delta^0, deltaext^0'=deltaext^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 41: l1 -> l1 : delta^0'=delta^0, delta_new^0'=delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 42: l1 -> l1 : delta^0'=delta^0, delta_new^0'=delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 43: l1 -> l1 : delta^0'=-1+delta^0, delta_new^0'=-1+delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 4 44: l1 -> l1 : delta^0'=-1+delta^0, delta_new^0'=-1+delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 4 45: l1 -> l1 : delta^0'=1+delta^0, delta_new^0'=1+delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 46: l1 -> l1 : delta^0'=1+delta^0, delta_new^0'=1+delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 47: l1 -> l1 : delta^0'=delta^0, delta_new^0'=delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 48: l1 -> l1 : delta^0'=delta^0, delta_new^0'=delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 49: l1 -> l1 : delta^0'=-1+delta^0, delta_new^0'=-1+delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 4 50: l1 -> l1 : delta^0'=-1+delta^0, delta_new^0'=-1+delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 4 51: l1 -> l1 : delta^0'=1+delta^0, delta_new^0'=1+delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 52: l1 -> l1 : delta^0'=1+delta^0, delta_new^0'=1+delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 16: l6 -> l1 : [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 ], cost: 2 Accelerating simple loops of location 2. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 37: l1 -> l1 : delta^0'=-1+delta^0, delta_new^0'=-1+delta^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 4 38: l1 -> l1 : delta^0'=1+delta^0, delta_new^0'=1+delta^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 39: l1 -> l1 : delta^0'=-1+delta^0, delta_new^0'=-1+delta^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 4 40: l1 -> l1 : delta^0'=1+delta^0, delta_new^0'=1+delta^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 41: l1 -> l1 : delta_new^0'=delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 42: l1 -> l1 : delta_new^0'=delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 44: l1 -> l1 : delta^0'=-1+delta^0, delta_new^0'=-1+delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 4 46: l1 -> l1 : delta^0'=1+delta^0, delta_new^0'=1+delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 47: l1 -> l1 : delta_new^0'=delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 48: l1 -> l1 : delta_new^0'=delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 50: l1 -> l1 : delta^0'=-1+delta^0, delta_new^0'=-1+delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 4 52: l1 -> l1 : delta^0'=1+delta^0, delta_new^0'=1+delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 Accelerated rule 37 with metering function meter (where 2*meter==-1-deltaext^0-wntext^0+2*delta^0), yielding the new rule 53. Accelerated rule 38 with metering function meter_1 (where 2*meter_1==deltaext^0+wntext^0-2*delta^0), yielding the new rule 54. Accelerated rule 39 with metering function meter_2 (where 2*meter_2==-1-deltaext^0-wntext^0+2*delta^0), yielding the new rule 55. Accelerated rule 40 with metering function meter_3 (where 2*meter_3==deltaext^0+wntext^0-2*delta^0), yielding the new rule 56. Accelerated rule 41 with metering function 1+deltaext^0+wntext^0-2*delta^0, yielding the new rule 57. Accelerated rule 42 with metering function deltaext^0+wntext^0-2*delta^0, yielding the new rule 58. Found no metering function for rule 44. Found no metering function for rule 46. Accelerated rule 47 with metering function -1-deltaext^0-wntext^0+2*delta^0, yielding the new rule 59. Accelerated rule 48 with metering function -deltaext^0-wntext^0+2*delta^0, yielding the new rule 60. Found no metering function for rule 50. Found no metering function for rule 52. Nested simple loops 44 (outer loop) and 53 (inner loop) with metering function meter_4 (where 2*meter_4==-5-wnt^0+2*deltaext^0), resulting in the new rules: 61. Nested simple loops 50 (outer loop) and 53 (inner loop) with metering function meter_5 (where 2*meter_5==1+wnt^0-2*deltaext^0), resulting in the new rules: 62. Nested simple loops 46 (outer loop) and 54 (inner loop) with metering function meter_6 (where 2*meter_6==-5-wnt^0+2*deltaext^0), resulting in the new rules: 63. Nested simple loops 52 (outer loop) and 54 (inner loop) with metering function meter_7 (where 2*meter_7==1+wnt^0-2*deltaext^0), resulting in the new rules: 64. Nested simple loops 44 (outer loop) and 55 (inner loop) with metering function meter_8 (where 2*meter_8==-4-wnt^0+2*deltaext^0), resulting in the new rules: 65. Nested simple loops 50 (outer loop) and 55 (inner loop) with metering function meter_9 (where 2*meter_9==wnt^0-2*deltaext^0), resulting in the new rules: 66. Nested simple loops 46 (outer loop) and 56 (inner loop) with metering function meter_10 (where 2*meter_10==-4-wnt^0+2*deltaext^0), resulting in the new rules: 67. Nested simple loops 52 (outer loop) and 56 (inner loop) with metering function meter_11 (where 2*meter_11==wnt^0-2*deltaext^0), resulting in the new rules: 68. Removing the simple loops: 37 38 39 40 41 42 44 46 47 48 50 52. Accelerated all simple loops using metering functions (where possible): Start location: l6 53: l1 -> l1 : delta^0'=delta^0-meter, delta_new^0'=delta^0-meter, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 && 2*meter==-1-deltaext^0-wntext^0+2*delta^0 && meter>=1 ], cost: 4*meter 54: l1 -> l1 : delta^0'=meter_1+delta^0, delta_new^0'=meter_1+delta^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 && 2*meter_1==deltaext^0+wntext^0-2*delta^0 && meter_1>=1 ], cost: 4*meter_1 55: l1 -> l1 : delta^0'=-meter_2+delta^0, delta_new^0'=-meter_2+delta^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 && 2*meter_2==-1-deltaext^0-wntext^0+2*delta^0 && meter_2>=1 ], cost: 4*meter_2 56: l1 -> l1 : delta^0'=delta^0+meter_3, delta_new^0'=delta^0+meter_3, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 && 2*meter_3==deltaext^0+wntext^0-2*delta^0 && meter_3>=1 ], cost: 4*meter_3 57: l1 -> l1 : delta_new^0'=delta^0, deltaext^0'=-1-wntext^0+2*delta^0, deltaext_new^0'=-1-wntext^0+2*delta^0, [ 3+wnt^0<=-1+2*deltaext^0 && 1+deltaext^0+wntext^0-2*delta^0==0 && 1+deltaext^0+wntext^0-2*delta^0>=1 ], cost: 4+4*deltaext^0+4*wntext^0-8*delta^0 58: l1 -> l1 : delta_new^0'=delta^0, deltaext^0'=-wntext^0+2*delta^0, deltaext_new^0'=-wntext^0+2*delta^0, [ 3+wnt^0<=-1+2*deltaext^0 && deltaext^0+wntext^0-2*delta^0==0 && deltaext^0+wntext^0-2*delta^0>=1 ], cost: 4*deltaext^0+4*wntext^0-8*delta^0 59: l1 -> l1 : delta_new^0'=delta^0, deltaext^0'=-1-wntext^0+2*delta^0, deltaext_new^0'=-1-wntext^0+2*delta^0, [ 1+2*deltaext^0<=2+wnt^0 && 1+deltaext^0+wntext^0-2*delta^0==0 && -1-deltaext^0-wntext^0+2*delta^0>=1 ], cost: -4-4*deltaext^0-4*wntext^0+8*delta^0 60: l1 -> l1 : delta_new^0'=delta^0, deltaext^0'=-wntext^0+2*delta^0, deltaext_new^0'=-wntext^0+2*delta^0, [ 1+2*deltaext^0<=2+wnt^0 && deltaext^0+wntext^0-2*delta^0==0 && -deltaext^0-wntext^0+2*delta^0>=1 ], cost: -4*deltaext^0-4*wntext^0+8*delta^0 61: l1 -> l1 : delta^0'=-meter_4+delta^0-meter_4*meter, delta_new^0'=-meter_4+delta^0-meter_4*meter, deltaext^0'=-meter_4+deltaext^0, deltaext_new^0'=-meter_4+deltaext^0, [ 5+wnt^0-2*deltaext^0==0 && deltaext^0+wntext^0<=-3+2*delta^0 && 2*meter==-2-deltaext^0-wntext^0+2*delta^0 && meter>=1 && 2*meter_4==-5-wnt^0+2*deltaext^0 && meter_4>=1 ], cost: 4*meter_4+4*meter_4*meter 62: l1 -> l1 : delta^0'=delta^0-meter_5*meter-meter_5, delta_new^0'=delta^0-meter_5*meter-meter_5, deltaext^0'=deltaext^0+meter_5, deltaext_new^0'=deltaext^0+meter_5, [ 1+wnt^0-2*deltaext^0==0 && 2+deltaext^0+wntext^0<=-3+2*delta^0 && 2*meter==-4-deltaext^0-wntext^0+2*delta^0 && meter>=1 && 2*meter_5==1+wnt^0-2*deltaext^0 && meter_5>=1 ], cost: 4*meter_5*meter+4*meter_5 63: l1 -> l1 : delta^0'=meter_1*meter_6+delta^0+meter_6, delta_new^0'=meter_1*meter_6+delta^0+meter_6, deltaext^0'=deltaext^0-meter_6, deltaext_new^0'=deltaext^0-meter_6, [ 5+wnt^0-2*deltaext^0==0 && 3+2*delta^0<=-1+deltaext^0+wntext^0 && 2*meter_1==-3+deltaext^0+wntext^0-2*delta^0 && meter_1>=1 && 2*meter_6==-5-wnt^0+2*deltaext^0 && meter_6>=1 ], cost: 4*meter_1*meter_6+4*meter_6 64: l1 -> l1 : delta^0'=meter_7+delta^0+meter_1*meter_7, delta_new^0'=meter_7+delta^0+meter_1*meter_7, deltaext^0'=deltaext^0+meter_7, deltaext_new^0'=deltaext^0+meter_7, [ 1+wnt^0-2*deltaext^0==0 && 3+2*delta^0<=1+deltaext^0+wntext^0 && 2*meter_1==-1+deltaext^0+wntext^0-2*delta^0 && meter_1>=1 && 2*meter_7==1+wnt^0-2*deltaext^0 && meter_7>=1 ], cost: 4*meter_7+4*meter_1*meter_7 65: l1 -> l1 : delta^0'=delta^0-meter_8-meter_2*meter_8, delta_new^0'=delta^0-meter_8-meter_2*meter_8, deltaext^0'=deltaext^0-meter_8, deltaext_new^0'=deltaext^0-meter_8, [ 4+wnt^0-2*deltaext^0==0 && deltaext^0+wntext^0<=-3+2*delta^0 && 2*meter_2==-2-deltaext^0-wntext^0+2*delta^0 && meter_2>=1 && 2*meter_8==-4-wnt^0+2*deltaext^0 && meter_8>=1 ], cost: 4*meter_8+4*meter_2*meter_8 66: l1 -> l1 : delta^0'=-meter_2*meter_9+delta^0-meter_9, delta_new^0'=-meter_2*meter_9+delta^0-meter_9, deltaext^0'=deltaext^0+meter_9, deltaext_new^0'=deltaext^0+meter_9, [ wnt^0-2*deltaext^0==0 && 2+deltaext^0+wntext^0<=-3+2*delta^0 && 2*meter_2==-4-deltaext^0-wntext^0+2*delta^0 && meter_2>=1 && 2*meter_9==wnt^0-2*deltaext^0 && meter_9>=1 ], cost: 4*meter_2*meter_9+4*meter_9 67: l1 -> l1 : delta^0'=delta^0+meter_3*meter_10+meter_10, delta_new^0'=delta^0+meter_3*meter_10+meter_10, deltaext^0'=deltaext^0-meter_10, deltaext_new^0'=deltaext^0-meter_10, [ 4+wnt^0-2*deltaext^0==0 && 3+2*delta^0<=-1+deltaext^0+wntext^0 && 2*meter_3==-3+deltaext^0+wntext^0-2*delta^0 && meter_3>=1 && 2*meter_10==-4-wnt^0+2*deltaext^0 && meter_10>=1 ], cost: 4*meter_3*meter_10+4*meter_10 68: l1 -> l1 : delta^0'=meter_11*meter_3+delta^0+meter_11, delta_new^0'=meter_11*meter_3+delta^0+meter_11, deltaext^0'=deltaext^0+meter_11, deltaext_new^0'=deltaext^0+meter_11, [ wnt^0-2*deltaext^0==0 && 3+2*delta^0<=1+deltaext^0+wntext^0 && 2*meter_3==-1+deltaext^0+wntext^0-2*delta^0 && meter_3>=1 && 2*meter_11==wnt^0-2*deltaext^0 && meter_11>=1 ], cost: 4*meter_11*meter_3+4*meter_11 16: l6 -> l1 : [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: l6 16: l6 -> l1 : [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 ], cost: 2 69: l6 -> l1 : delta^0'=delta^0-meter, delta_new^0'=delta^0-meter, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 && 2*meter==-1-deltaext^0-wntext^0+2*delta^0 && meter>=1 ], cost: 2+4*meter 70: l6 -> l1 : delta^0'=meter_1+delta^0, delta_new^0'=meter_1+delta^0, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 3+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 && 2*meter_1==deltaext^0+wntext^0-2*delta^0 && meter_1>=1 ], cost: 2+4*meter_1 71: l6 -> l1 : delta^0'=-meter_2+delta^0, delta_new^0'=-meter_2+delta^0, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 2+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 && 2*meter_2==-1-deltaext^0-wntext^0+2*delta^0 && meter_2>=1 ], cost: 2+4*meter_2 72: l6 -> l1 : delta^0'=delta^0+meter_3, delta_new^0'=delta^0+meter_3, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 2+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 && 2*meter_3==deltaext^0+wntext^0-2*delta^0 && meter_3>=1 ], cost: 2+4*meter_3 Removed unreachable locations (and leaf rules with constant cost): Start location: l6 69: l6 -> l1 : delta^0'=delta^0-meter, delta_new^0'=delta^0-meter, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 && 2*meter==-1-deltaext^0-wntext^0+2*delta^0 && meter>=1 ], cost: 2+4*meter 70: l6 -> l1 : delta^0'=meter_1+delta^0, delta_new^0'=meter_1+delta^0, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 3+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 && 2*meter_1==deltaext^0+wntext^0-2*delta^0 && meter_1>=1 ], cost: 2+4*meter_1 71: l6 -> l1 : delta^0'=-meter_2+delta^0, delta_new^0'=-meter_2+delta^0, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 2+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 && 2*meter_2==-1-deltaext^0-wntext^0+2*delta^0 && meter_2>=1 ], cost: 2+4*meter_2 72: l6 -> l1 : delta^0'=delta^0+meter_3, delta_new^0'=delta^0+meter_3, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 2+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 && 2*meter_3==deltaext^0+wntext^0-2*delta^0 && meter_3>=1 ], cost: 2+4*meter_3 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l6 69: l6 -> l1 : delta^0'=delta^0-meter, delta_new^0'=delta^0-meter, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 && 2*meter==-1-deltaext^0-wntext^0+2*delta^0 && meter>=1 ], cost: 2+4*meter 70: l6 -> l1 : delta^0'=meter_1+delta^0, delta_new^0'=meter_1+delta^0, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 3+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 && 2*meter_1==deltaext^0+wntext^0-2*delta^0 && meter_1>=1 ], cost: 2+4*meter_1 71: l6 -> l1 : delta^0'=-meter_2+delta^0, delta_new^0'=-meter_2+delta^0, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 2+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 && 2*meter_2==-1-deltaext^0-wntext^0+2*delta^0 && meter_2>=1 ], cost: 2+4*meter_2 72: l6 -> l1 : delta^0'=delta^0+meter_3, delta_new^0'=delta^0+meter_3, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 2+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 && 2*meter_3==deltaext^0+wntext^0-2*delta^0 && meter_3>=1 ], cost: 2+4*meter_3 Computing asymptotic complexity for rule 69 Simplified the guard: 69: l6 -> l1 : delta^0'=delta^0-meter, delta_new^0'=delta^0-meter, deltaext_new^0'=deltaext^0, [ 0<=wnt^0 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0<=-1+2*delta^0 && 2*meter==-1-deltaext^0-wntext^0+2*delta^0 ], cost: 2+4*meter Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 70 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 71 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 72 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [ delta^0==delta^post_16 && delta_new^0==delta_new^post_16 && deltaext^0==deltaext^post_16 && deltaext_new^0==deltaext_new^post_16 && deltext^0==deltext^post_16 && wnt^0==wnt^post_16 && wntext^0==wntext^post_16 ] WORST_CASE(Omega(1),?)