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. [accelerate] Removed some duplicate simple loops 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 backward acceleration, yielding the new rule 53. Accelerated rule 38 with backward acceleration, yielding the new rule 54. Accelerated rule 39 with backward acceleration, yielding the new rule 55. Accelerated rule 40 with backward acceleration, yielding the new rule 56. Failed to prove monotonicity of the guard of rule 41. Failed to prove monotonicity of the guard of rule 42. Accelerated rule 44 with backward acceleration, yielding the new rule 57. Accelerated rule 46 with backward acceleration, yielding the new rule 58. Failed to prove monotonicity of the guard of rule 47. Failed to prove monotonicity of the guard of rule 48. Accelerated rule 50 with backward acceleration, yielding the new rule 59. Accelerated rule 52 with backward acceleration, yielding the new rule 60. [accelerate] Nesting with 12 inner and 12 outer candidates Nested simple loops 44 (outer loop) and 41 (inner loop) with Rule(2 | 1+deltaext^0+wntext^0-2*delta^0==0, k_12>=1, 3+wnt^0<=1-4*k_12+2*deltaext^0, | 8*k_12 || 2 | 0=-k_12+delta^0, 1=-k_12+delta^0, 2=-2*k_12+deltaext^0, 3=-2*k_12+deltaext^0, ), resulting in the new rules: 61, 62. Nested simple loops 52 (outer loop) and 48 (inner loop) with Rule(2 | deltaext^0+wntext^0-2*delta^0==0, k_15>=1, -1+2*deltaext^0+4*k_15<=2+wnt^0, | 8*k_15 || 2 | 0=k_15+delta^0, 1=k_15+delta^0, 2=deltaext^0+2*k_15, 3=deltaext^0+2*k_15, ), resulting in the new rules: 63, 64. Removing the simple loops: 37 38 39 40 44 46 50 52. Accelerated all simple loops using metering functions (where possible): Start location: l6 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 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 53: l1 -> l1 : delta^0'=-k+delta^0, delta_new^0'=-k+delta^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && k>=1 && 1+deltaext^0+wntext^0<=1-2*k+2*delta^0 ], cost: 4*k 54: l1 -> l1 : delta^0'=k_1+delta^0, delta_new^0'=k_1+delta^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && k_1>=1 && -1+2*k_1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4*k_1 55: l1 -> l1 : delta^0'=-k_2+delta^0, delta_new^0'=-k_2+delta^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && k_2>=1 && 1+deltaext^0+wntext^0<=1-2*k_2+2*delta^0 ], cost: 4*k_2 56: l1 -> l1 : delta^0'=k_3+delta^0, delta_new^0'=k_3+delta^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && k_3>=1 && -1+2*k_3+2*delta^0<=deltaext^0+wntext^0 ], cost: 4*k_3 57: l1 -> l1 : delta^0'=-k_6+delta^0, delta_new^0'=-k_6+delta^0, deltaext^0'=deltaext^0-k_6, deltaext_new^0'=deltaext^0-k_6, [ k_6>=1 && 3+wnt^0<=1+2*deltaext^0-2*k_6 && 2+deltaext^0+wntext^0-k_6<=1-2*k_6+2*delta^0 ], cost: 4*k_6 58: l1 -> l1 : delta^0'=k_7+delta^0, delta_new^0'=k_7+delta^0, deltaext^0'=-k_7+deltaext^0, deltaext_new^0'=-k_7+deltaext^0, [ k_7>=1 && 3+wnt^0<=1-2*k_7+2*deltaext^0 && -1+2*k_7+2*delta^0<=1-k_7+deltaext^0+wntext^0 ], cost: 4*k_7 59: l1 -> l1 : delta^0'=-k_10+delta^0, delta_new^0'=-k_10+delta^0, deltaext^0'=k_10+deltaext^0, deltaext_new^0'=k_10+deltaext^0, [ k_10>=1 && -1+2*k_10+2*deltaext^0<=2+wnt^0 && k_10+deltaext^0+wntext^0<=1-2*k_10+2*delta^0 ], cost: 4*k_10 60: l1 -> l1 : delta^0'=delta^0+k_11, delta_new^0'=delta^0+k_11, deltaext^0'=deltaext^0+k_11, deltaext_new^0'=deltaext^0+k_11, [ k_11>=1 && -1+2*deltaext^0+2*k_11<=2+wnt^0 && -1+2*delta^0+2*k_11<=-1+deltaext^0+wntext^0+k_11 ], cost: 4*k_11 61: l1 -> l1 : delta^0'=-k_12+delta^0, delta_new^0'=-k_12+delta^0, deltaext^0'=-2*k_12+deltaext^0, deltaext_new^0'=-2*k_12+deltaext^0, [ 1+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=1-4*k_12+2*deltaext^0 ], cost: 8*k_12 62: l1 -> l1 : delta^0'=-1-k_12+delta^0, delta_new^0'=-1-k_12+delta^0, deltaext^0'=-1-2*k_12+deltaext^0, deltaext_new^0'=-1-2*k_12+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 && 2+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=-1-4*k_12+2*deltaext^0 ], cost: 4+8*k_12 63: l1 -> l1 : delta^0'=k_15+delta^0, delta_new^0'=k_15+delta^0, deltaext^0'=deltaext^0+2*k_15, deltaext_new^0'=deltaext^0+2*k_15, [ deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && -1+2*deltaext^0+4*k_15<=2+wnt^0 ], cost: 8*k_15 64: l1 -> l1 : delta^0'=1+k_15+delta^0, delta_new^0'=1+k_15+delta^0, deltaext^0'=1+deltaext^0+2*k_15, deltaext_new^0'=1+deltaext^0+2*k_15, [ 1+2*deltaext^0<=2+wnt^0 && -1+deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && 1+2*deltaext^0+4*k_15<=2+wnt^0 ], cost: 4+8*k_15 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 65: l6 -> l1 : delta_new^0'=delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+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<=-1+2*deltaext^0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 6 66: l6 -> l1 : delta_new^0'=delta^0, deltaext^0'=-1+deltaext^0, deltaext_new^0'=-1+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<=-1+2*deltaext^0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 6 67: l6 -> l1 : delta_new^0'=delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+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 && 1+2*deltaext^0<=2+wnt^0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 6 68: l6 -> l1 : delta_new^0'=delta^0, deltaext^0'=1+deltaext^0, deltaext_new^0'=1+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 && 1+2*deltaext^0<=2+wnt^0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 6 69: l6 -> l1 : delta^0'=-k+delta^0, delta_new^0'=-k+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 && k>=1 && 1+deltaext^0+wntext^0<=1-2*k+2*delta^0 ], cost: 2+4*k 70: l6 -> l1 : delta^0'=k_1+delta^0, delta_new^0'=k_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 && k_1>=1 && -1+2*k_1+2*delta^0<=deltaext^0+wntext^0 ], cost: 2+4*k_1 71: l6 -> l1 : delta^0'=-k_2+delta^0, delta_new^0'=-k_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 && k_2>=1 && 1+deltaext^0+wntext^0<=1-2*k_2+2*delta^0 ], cost: 2+4*k_2 72: l6 -> l1 : delta^0'=k_3+delta^0, delta_new^0'=k_3+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 && k_3>=1 && -1+2*k_3+2*delta^0<=deltaext^0+wntext^0 ], cost: 2+4*k_3 73: l6 -> l1 : delta^0'=-k_6+delta^0, delta_new^0'=-k_6+delta^0, deltaext^0'=deltaext^0-k_6, deltaext_new^0'=deltaext^0-k_6, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && k_6>=1 && 3+wnt^0<=1+2*deltaext^0-2*k_6 && 2+deltaext^0+wntext^0-k_6<=1-2*k_6+2*delta^0 ], cost: 2+4*k_6 74: l6 -> l1 : delta^0'=k_7+delta^0, delta_new^0'=k_7+delta^0, deltaext^0'=-k_7+deltaext^0, deltaext_new^0'=-k_7+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 && k_7>=1 && 3+wnt^0<=1-2*k_7+2*deltaext^0 && -1+2*k_7+2*delta^0<=1-k_7+deltaext^0+wntext^0 ], cost: 2+4*k_7 75: l6 -> l1 : delta^0'=-k_10+delta^0, delta_new^0'=-k_10+delta^0, deltaext^0'=k_10+deltaext^0, deltaext_new^0'=k_10+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 && k_10>=1 && -1+2*k_10+2*deltaext^0<=2+wnt^0 && k_10+deltaext^0+wntext^0<=1-2*k_10+2*delta^0 ], cost: 2+4*k_10 76: l6 -> l1 : delta^0'=delta^0+k_11, delta_new^0'=delta^0+k_11, deltaext^0'=deltaext^0+k_11, deltaext_new^0'=deltaext^0+k_11, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && k_11>=1 && -1+2*deltaext^0+2*k_11<=2+wnt^0 && -1+2*delta^0+2*k_11<=-1+deltaext^0+wntext^0+k_11 ], cost: 2+4*k_11 77: l6 -> l1 : delta^0'=-k_12+delta^0, delta_new^0'=-k_12+delta^0, deltaext^0'=-2*k_12+deltaext^0, deltaext_new^0'=-2*k_12+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 && 1+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=1-4*k_12+2*deltaext^0 ], cost: 2+8*k_12 78: l6 -> l1 : delta^0'=-1-k_12+delta^0, delta_new^0'=-1-k_12+delta^0, deltaext^0'=-1-2*k_12+deltaext^0, deltaext_new^0'=-1-2*k_12+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<=-1+2*deltaext^0 && 2+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=-1-4*k_12+2*deltaext^0 ], cost: 6+8*k_12 79: l6 -> l1 : delta^0'=k_15+delta^0, delta_new^0'=k_15+delta^0, deltaext^0'=deltaext^0+2*k_15, deltaext_new^0'=deltaext^0+2*k_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 && deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && -1+2*deltaext^0+4*k_15<=2+wnt^0 ], cost: 2+8*k_15 80: l6 -> l1 : delta^0'=1+k_15+delta^0, delta_new^0'=1+k_15+delta^0, deltaext^0'=1+deltaext^0+2*k_15, deltaext_new^0'=1+deltaext^0+2*k_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 && 1+2*deltaext^0<=2+wnt^0 && -1+deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && 1+2*deltaext^0+4*k_15<=2+wnt^0 ], cost: 6+8*k_15 Removed unreachable locations (and leaf rules with constant cost): Start location: l6 69: l6 -> l1 : delta^0'=-k+delta^0, delta_new^0'=-k+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 && k>=1 && 1+deltaext^0+wntext^0<=1-2*k+2*delta^0 ], cost: 2+4*k 70: l6 -> l1 : delta^0'=k_1+delta^0, delta_new^0'=k_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 && k_1>=1 && -1+2*k_1+2*delta^0<=deltaext^0+wntext^0 ], cost: 2+4*k_1 71: l6 -> l1 : delta^0'=-k_2+delta^0, delta_new^0'=-k_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 && k_2>=1 && 1+deltaext^0+wntext^0<=1-2*k_2+2*delta^0 ], cost: 2+4*k_2 72: l6 -> l1 : delta^0'=k_3+delta^0, delta_new^0'=k_3+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 && k_3>=1 && -1+2*k_3+2*delta^0<=deltaext^0+wntext^0 ], cost: 2+4*k_3 73: l6 -> l1 : delta^0'=-k_6+delta^0, delta_new^0'=-k_6+delta^0, deltaext^0'=deltaext^0-k_6, deltaext_new^0'=deltaext^0-k_6, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && k_6>=1 && 3+wnt^0<=1+2*deltaext^0-2*k_6 && 2+deltaext^0+wntext^0-k_6<=1-2*k_6+2*delta^0 ], cost: 2+4*k_6 74: l6 -> l1 : delta^0'=k_7+delta^0, delta_new^0'=k_7+delta^0, deltaext^0'=-k_7+deltaext^0, deltaext_new^0'=-k_7+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 && k_7>=1 && 3+wnt^0<=1-2*k_7+2*deltaext^0 && -1+2*k_7+2*delta^0<=1-k_7+deltaext^0+wntext^0 ], cost: 2+4*k_7 75: l6 -> l1 : delta^0'=-k_10+delta^0, delta_new^0'=-k_10+delta^0, deltaext^0'=k_10+deltaext^0, deltaext_new^0'=k_10+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 && k_10>=1 && -1+2*k_10+2*deltaext^0<=2+wnt^0 && k_10+deltaext^0+wntext^0<=1-2*k_10+2*delta^0 ], cost: 2+4*k_10 76: l6 -> l1 : delta^0'=delta^0+k_11, delta_new^0'=delta^0+k_11, deltaext^0'=deltaext^0+k_11, deltaext_new^0'=deltaext^0+k_11, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && k_11>=1 && -1+2*deltaext^0+2*k_11<=2+wnt^0 && -1+2*delta^0+2*k_11<=-1+deltaext^0+wntext^0+k_11 ], cost: 2+4*k_11 77: l6 -> l1 : delta^0'=-k_12+delta^0, delta_new^0'=-k_12+delta^0, deltaext^0'=-2*k_12+deltaext^0, deltaext_new^0'=-2*k_12+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 && 1+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=1-4*k_12+2*deltaext^0 ], cost: 2+8*k_12 78: l6 -> l1 : delta^0'=-1-k_12+delta^0, delta_new^0'=-1-k_12+delta^0, deltaext^0'=-1-2*k_12+deltaext^0, deltaext_new^0'=-1-2*k_12+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<=-1+2*deltaext^0 && 2+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=-1-4*k_12+2*deltaext^0 ], cost: 6+8*k_12 79: l6 -> l1 : delta^0'=k_15+delta^0, delta_new^0'=k_15+delta^0, deltaext^0'=deltaext^0+2*k_15, deltaext_new^0'=deltaext^0+2*k_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 && deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && -1+2*deltaext^0+4*k_15<=2+wnt^0 ], cost: 2+8*k_15 80: l6 -> l1 : delta^0'=1+k_15+delta^0, delta_new^0'=1+k_15+delta^0, deltaext^0'=1+deltaext^0+2*k_15, deltaext_new^0'=1+deltaext^0+2*k_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 && 1+2*deltaext^0<=2+wnt^0 && -1+deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && 1+2*deltaext^0+4*k_15<=2+wnt^0 ], cost: 6+8*k_15 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l6 69: l6 -> l1 : delta^0'=-k+delta^0, delta_new^0'=-k+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 && k>=1 && 1+deltaext^0+wntext^0<=1-2*k+2*delta^0 ], cost: 2+4*k 70: l6 -> l1 : delta^0'=k_1+delta^0, delta_new^0'=k_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 && k_1>=1 && -1+2*k_1+2*delta^0<=deltaext^0+wntext^0 ], cost: 2+4*k_1 71: l6 -> l1 : delta^0'=-k_2+delta^0, delta_new^0'=-k_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 && k_2>=1 && 1+deltaext^0+wntext^0<=1-2*k_2+2*delta^0 ], cost: 2+4*k_2 72: l6 -> l1 : delta^0'=k_3+delta^0, delta_new^0'=k_3+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 && k_3>=1 && -1+2*k_3+2*delta^0<=deltaext^0+wntext^0 ], cost: 2+4*k_3 73: l6 -> l1 : delta^0'=-k_6+delta^0, delta_new^0'=-k_6+delta^0, deltaext^0'=deltaext^0-k_6, deltaext_new^0'=deltaext^0-k_6, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && k_6>=1 && 3+wnt^0<=1+2*deltaext^0-2*k_6 && 2+deltaext^0+wntext^0-k_6<=1-2*k_6+2*delta^0 ], cost: 2+4*k_6 74: l6 -> l1 : delta^0'=k_7+delta^0, delta_new^0'=k_7+delta^0, deltaext^0'=-k_7+deltaext^0, deltaext_new^0'=-k_7+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 && k_7>=1 && 3+wnt^0<=1-2*k_7+2*deltaext^0 && -1+2*k_7+2*delta^0<=1-k_7+deltaext^0+wntext^0 ], cost: 2+4*k_7 75: l6 -> l1 : delta^0'=-k_10+delta^0, delta_new^0'=-k_10+delta^0, deltaext^0'=k_10+deltaext^0, deltaext_new^0'=k_10+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 && k_10>=1 && -1+2*k_10+2*deltaext^0<=2+wnt^0 && k_10+deltaext^0+wntext^0<=1-2*k_10+2*delta^0 ], cost: 2+4*k_10 76: l6 -> l1 : delta^0'=delta^0+k_11, delta_new^0'=delta^0+k_11, deltaext^0'=deltaext^0+k_11, deltaext_new^0'=deltaext^0+k_11, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && k_11>=1 && -1+2*deltaext^0+2*k_11<=2+wnt^0 && -1+2*delta^0+2*k_11<=-1+deltaext^0+wntext^0+k_11 ], cost: 2+4*k_11 77: l6 -> l1 : delta^0'=-k_12+delta^0, delta_new^0'=-k_12+delta^0, deltaext^0'=-2*k_12+deltaext^0, deltaext_new^0'=-2*k_12+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 && 1+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=1-4*k_12+2*deltaext^0 ], cost: 2+8*k_12 78: l6 -> l1 : delta^0'=-1-k_12+delta^0, delta_new^0'=-1-k_12+delta^0, deltaext^0'=-1-2*k_12+deltaext^0, deltaext_new^0'=-1-2*k_12+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<=-1+2*deltaext^0 && 2+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=-1-4*k_12+2*deltaext^0 ], cost: 6+8*k_12 79: l6 -> l1 : delta^0'=k_15+delta^0, delta_new^0'=k_15+delta^0, deltaext^0'=deltaext^0+2*k_15, deltaext_new^0'=deltaext^0+2*k_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 && deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && -1+2*deltaext^0+4*k_15<=2+wnt^0 ], cost: 2+8*k_15 80: l6 -> l1 : delta^0'=1+k_15+delta^0, delta_new^0'=1+k_15+delta^0, deltaext^0'=1+deltaext^0+2*k_15, deltaext_new^0'=1+deltaext^0+2*k_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 && 1+2*deltaext^0<=2+wnt^0 && -1+deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && 1+2*deltaext^0+4*k_15<=2+wnt^0 ], cost: 6+8*k_15 Computing asymptotic complexity for rule 69 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 70 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 71 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 72 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 73 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 74 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 75 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 76 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 77 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 79 Simplified the guard: 79: l6 -> l1 : delta^0'=k_15+delta^0, delta_new^0'=k_15+delta^0, deltaext^0'=deltaext^0+2*k_15, deltaext_new^0'=deltaext^0+2*k_15, [ wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && -1+2*deltaext^0+4*k_15<=2+wnt^0 ], cost: 2+8*k_15 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 78 Simplified the guard: 78: l6 -> l1 : delta^0'=-1-k_12+delta^0, delta_new^0'=-1-k_12+delta^0, deltaext^0'=-1-2*k_12+deltaext^0, deltaext_new^0'=-1-2*k_12+deltaext^0, [ 0<=wnt^0 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && 2+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=-1-4*k_12+2*deltaext^0 ], cost: 6+8*k_12 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 80 Simplified the guard: 80: l6 -> l1 : delta^0'=1+k_15+delta^0, delta_new^0'=1+k_15+delta^0, deltaext^0'=1+deltaext^0+2*k_15, deltaext_new^0'=1+deltaext^0+2*k_15, [ wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && -1+deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && 1+2*deltaext^0+4*k_15<=2+wnt^0 ], cost: 6+8*k_15 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),?)