NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l6 0: l0 -> l2 : __disjvr_0^0'=__disjvr_0^post_1, __disjvr_1^0'=__disjvr_1^post_1, 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, [ __disjvr_0^post_1==__disjvr_0^0 && __disjvr_0^0==__disjvr_0^post_1 && __disjvr_1^0==__disjvr_1^post_1 && 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 2: l0 -> l3 : __disjvr_0^0'=__disjvr_0^post_3, __disjvr_1^0'=__disjvr_1^post_3, 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, [ __disjvr_1^post_3==__disjvr_1^0 && __disjvr_0^0==__disjvr_0^post_3 && __disjvr_1^0==__disjvr_1^post_3 && 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 ], cost: 1 1: l2 -> l1 : __disjvr_0^0'=__disjvr_0^post_2, __disjvr_1^0'=__disjvr_1^post_2, 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, [ deltaext^post_2==deltaext_new^0 && delta^post_2==delta_new^0 && __disjvr_0^0==__disjvr_0^post_2 && __disjvr_1^0==__disjvr_1^post_2 && delta_new^0==delta_new^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 8: l1 -> l4 : __disjvr_0^0'=__disjvr_0^post_9, __disjvr_1^0'=__disjvr_1^post_9, 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, [ 2+wnt^0<=-1+2*deltaext^0 && -1+2*deltaext^0<=2+wnt^0 && deltaext_new^post_9==deltaext^0 && __disjvr_0^0==__disjvr_0^post_9 && __disjvr_1^0==__disjvr_1^post_9 && delta^0==delta^post_9 && delta_new^0==delta_new^post_9 && deltaext^0==deltaext^post_9 && deltext^0==deltext^post_9 && wnt^0==wnt^post_9 && wntext^0==wntext^post_9 ], cost: 1 9: l1 -> l4 : __disjvr_0^0'=__disjvr_0^post_10, __disjvr_1^0'=__disjvr_1^post_10, 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, [ 2+wnt^0<=2*deltaext^0 && 2*deltaext^0<=2+wnt^0 && deltaext_new^post_10==deltaext^0 && __disjvr_0^0==__disjvr_0^post_10 && __disjvr_1^0==__disjvr_1^post_10 && delta^0==delta^post_10 && delta_new^0==delta_new^post_10 && deltaext^0==deltaext^post_10 && deltext^0==deltext^post_10 && wnt^0==wnt^post_10 && wntext^0==wntext^post_10 ], cost: 1 10: l1 -> l4 : __disjvr_0^0'=__disjvr_0^post_11, __disjvr_1^0'=__disjvr_1^post_11, 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, [ 3+wnt^0<=-1+2*deltaext^0 && deltaext_new^post_11==-1+deltaext^0 && __disjvr_0^0==__disjvr_0^post_11 && __disjvr_1^0==__disjvr_1^post_11 && 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 : __disjvr_0^0'=__disjvr_0^post_12, __disjvr_1^0'=__disjvr_1^post_12, 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, [ 1+2*deltaext^0<=2+wnt^0 && deltaext_new^post_12==1+deltaext^0 && __disjvr_0^0==__disjvr_0^post_12 && __disjvr_1^0==__disjvr_1^post_12 && 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 3: l3 -> l1 : __disjvr_0^0'=__disjvr_0^post_4, __disjvr_1^0'=__disjvr_1^post_4, 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, [ deltaext^post_4==deltaext_new^0 && delta^post_4==delta_new^0 && __disjvr_0^0==__disjvr_0^post_4 && __disjvr_1^0==__disjvr_1^post_4 && delta_new^0==delta_new^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: l4 -> l0 : __disjvr_0^0'=__disjvr_0^post_5, __disjvr_1^0'=__disjvr_1^post_5, 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, [ deltaext^0+wntext^0<=-1+2*delta^0 && -1+2*delta^0<=deltaext^0+wntext^0 && delta_new^post_5==delta^0 && __disjvr_0^0==__disjvr_0^post_5 && __disjvr_1^0==__disjvr_1^post_5 && delta^0==delta^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 5: l4 -> l0 : __disjvr_0^0'=__disjvr_0^post_6, __disjvr_1^0'=__disjvr_1^post_6, 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^0+wntext^0<=2*delta^0 && 2*delta^0<=deltaext^0+wntext^0 && delta_new^post_6==delta^0 && __disjvr_0^0==__disjvr_0^post_6 && __disjvr_1^0==__disjvr_1^post_6 && delta^0==delta^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 ], cost: 1 6: l4 -> l0 : __disjvr_0^0'=__disjvr_0^post_7, __disjvr_1^0'=__disjvr_1^post_7, 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, [ 1+deltaext^0+wntext^0<=-1+2*delta^0 && delta_new^post_7==-1+delta^0 && __disjvr_0^0==__disjvr_0^post_7 && __disjvr_1^0==__disjvr_1^post_7 && 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 : __disjvr_0^0'=__disjvr_0^post_8, __disjvr_1^0'=__disjvr_1^post_8, 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, [ 1+2*delta^0<=deltaext^0+wntext^0 && delta_new^post_8==1+delta^0 && __disjvr_0^0==__disjvr_0^post_8 && __disjvr_1^0==__disjvr_1^post_8 && 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 12: l5 -> l1 : __disjvr_0^0'=__disjvr_0^post_13, __disjvr_1^0'=__disjvr_1^post_13, 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, [ 0<=wnt^0 && wnt^0<=3 && 0<=deltaext^0 && deltext^0<=3 && 0<=wntext^0 && wntext^0<=3 && 0<=delta^0 && delta^0<=3 && __disjvr_0^0==__disjvr_0^post_13 && __disjvr_1^0==__disjvr_1^post_13 && 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 ], cost: 1 13: l6 -> l5 : __disjvr_0^0'=__disjvr_0^post_14, __disjvr_1^0'=__disjvr_1^post_14, 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, [ __disjvr_0^0==__disjvr_0^post_14 && __disjvr_1^0==__disjvr_1^post_14 && 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 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 13: l6 -> l5 : __disjvr_0^0'=__disjvr_0^post_14, __disjvr_1^0'=__disjvr_1^post_14, 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, [ __disjvr_0^0==__disjvr_0^post_14 && __disjvr_1^0==__disjvr_1^post_14 && 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 ], cost: 1 Simplified all rules, resulting in: Start location: l6 0: l0 -> l2 : [], cost: 1 2: l0 -> l3 : [], cost: 1 1: l2 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [], cost: 1 8: l1 -> l4 : deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 ], cost: 1 9: l1 -> l4 : deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 ], cost: 1 10: l1 -> l4 : deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 ], cost: 1 11: l1 -> l4 : deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 ], cost: 1 3: l3 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [], cost: 1 4: l4 -> l0 : delta_new^0'=delta^0, [ 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 1 5: l4 -> l0 : delta_new^0'=delta^0, [ deltaext^0+wntext^0-2*delta^0==0 ], cost: 1 6: l4 -> l0 : delta_new^0'=-1+delta^0, [ 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 1 7: l4 -> l0 : delta_new^0'=1+delta^0, [ 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 1 12: 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 13: l6 -> l5 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l6 15: l0 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [], cost: 2 16: l0 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [], cost: 2 8: l1 -> l4 : deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 ], cost: 1 9: l1 -> l4 : deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 ], cost: 1 10: l1 -> l4 : deltaext_new^0'=-1+deltaext^0, [ 3+wnt^0<=-1+2*deltaext^0 ], cost: 1 11: l1 -> l4 : deltaext_new^0'=1+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 ], cost: 1 4: l4 -> l0 : delta_new^0'=delta^0, [ 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 1 5: l4 -> l0 : delta_new^0'=delta^0, [ deltaext^0+wntext^0-2*delta^0==0 ], cost: 1 6: l4 -> l0 : delta_new^0'=-1+delta^0, [ 1+deltaext^0+wntext^0<=-1+2*delta^0 ], cost: 1 7: l4 -> l0 : delta_new^0'=1+delta^0, [ 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 1 14: 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 15: l0 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^0, [], cost: 2 16: l0 -> l1 : delta^0'=delta_new^0, deltaext^0'=deltaext_new^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 14: 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: l1 -> l1 : delta^0'=delta^0, delta_new^0'=delta^0, deltaext^0'=deltaext^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 34: l1 -> l1 : delta^0'=delta^0, delta_new^0'=delta^0, deltaext^0'=deltaext^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 35: l1 -> l1 : delta^0'=delta^0, delta_new^0'=delta^0, deltaext^0'=deltaext^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 36: l1 -> l1 : delta^0'=delta^0, delta_new^0'=delta^0, deltaext^0'=deltaext^0, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 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+deltaext^0+wntext^0<=-1+2*delta^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, [ 3+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^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, [ 3+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'=deltaext^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==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'=deltaext^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 43: l1 -> l1 : delta^0'=delta^0, delta_new^0'=delta^0, deltaext^0'=deltaext^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 44: l1 -> l1 : delta^0'=delta^0, delta_new^0'=delta^0, deltaext^0'=deltaext^0, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: 4 45: 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 46: 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 47: 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 48: 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 49: 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 50: 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 51: 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 52: 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 53: 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 54: 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 55: 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 56: 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 57: 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 58: 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 59: 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 60: 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 61: 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 62: 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 63: 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 64: 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 14: 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: 34: l1 -> l1 : 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: 4 36: l1 -> l1 : 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: 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+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, [ 3+wnt^0-2*deltaext^0==0 && 1+2*delta^0<=deltaext^0+wntext^0 ], cost: 4 42: l1 -> l1 : 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: 4 44: l1 -> l1 : 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: 4 46: 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 48: 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 50: 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 52: 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 54: 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 56: 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 58: 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 60: 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 62: 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 64: 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 34 with non-termination, yielding the new rule 65. Accelerated rule 36 with non-termination, yielding the new rule 66. Accelerated rule 38 with backward acceleration, yielding the new rule 67. Accelerated rule 40 with backward acceleration, yielding the new rule 68. Accelerated rule 42 with non-termination, yielding the new rule 69. Accelerated rule 44 with non-termination, yielding the new rule 70. Accelerated rule 46 with backward acceleration, yielding the new rule 71. Accelerated rule 48 with backward acceleration, yielding the new rule 72. Failed to prove monotonicity of the guard of rule 50. Failed to prove monotonicity of the guard of rule 52. Accelerated rule 54 with backward acceleration, yielding the new rule 73. Accelerated rule 56 with backward acceleration, yielding the new rule 74. Failed to prove monotonicity of the guard of rule 58. Failed to prove monotonicity of the guard of rule 60. Accelerated rule 62 with backward acceleration, yielding the new rule 75. Accelerated rule 64 with backward acceleration, yielding the new rule 76. [accelerate] Nesting with 12 inner and 12 outer candidates Nested simple loops 54 (outer loop) and 50 (inner loop) with Rule(2 | 1+deltaext^0+wntext^0-2*delta^0==0, k_12>=1, 3+wnt^0<=1+2*deltaext^0-4*k_12, | 8*k_12 || 2 | 2=delta^0-k_12, 3=delta^0-k_12, 4=deltaext^0-2*k_12, 5=deltaext^0-2*k_12, ), resulting in the new rules: 77, 78. Nested simple loops 64 (outer loop) and 60 (inner loop) with Rule(2 | deltaext^0+wntext^0-2*delta^0==0, k_15>=1, -1+4*k_15+2*deltaext^0<=2+wnt^0, | 8*k_15 || 2 | 2=k_15+delta^0, 3=k_15+delta^0, 4=2*k_15+deltaext^0, 5=2*k_15+deltaext^0, ), resulting in the new rules: 79, 80. Removing the simple loops: 34 36 38 40 42 44 46 48 54 56 62 64. Accelerated all simple loops using metering functions (where possible): Start location: l6 50: 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 52: 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 58: 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 60: 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 65: l1 -> [7] : [ 3+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: NONTERM 66: l1 -> [7] : [ 3+wnt^0-2*deltaext^0==0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: NONTERM 67: 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 68: l1 -> l1 : delta^0'=delta^0+k_1, delta_new^0'=delta^0+k_1, deltaext_new^0'=deltaext^0, [ 3+wnt^0-2*deltaext^0==0 && k_1>=1 && -1+2*delta^0+2*k_1<=deltaext^0+wntext^0 ], cost: 4*k_1 69: l1 -> [7] : [ 2+wnt^0-2*deltaext^0==0 && 1+deltaext^0+wntext^0-2*delta^0==0 ], cost: NONTERM 70: l1 -> [7] : [ 2+wnt^0-2*deltaext^0==0 && deltaext^0+wntext^0-2*delta^0==0 ], cost: NONTERM 71: l1 -> l1 : delta^0'=delta^0-k_2, delta_new^0'=delta^0-k_2, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && k_2>=1 && 1+deltaext^0+wntext^0<=1+2*delta^0-2*k_2 ], cost: 4*k_2 72: l1 -> l1 : delta^0'=delta^0+k_3, delta_new^0'=delta^0+k_3, deltaext_new^0'=deltaext^0, [ 2+wnt^0-2*deltaext^0==0 && k_3>=1 && -1+2*delta^0+2*k_3<=deltaext^0+wntext^0 ], cost: 4*k_3 73: l1 -> l1 : delta^0'=delta^0-k_6, delta_new^0'=delta^0-k_6, 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*delta^0-2*k_6 ], cost: 4*k_6 74: l1 -> l1 : delta^0'=delta^0+k_7, delta_new^0'=delta^0+k_7, deltaext^0'=deltaext^0-k_7, deltaext_new^0'=deltaext^0-k_7, [ k_7>=1 && 3+wnt^0<=1+2*deltaext^0-2*k_7 && -1+2*delta^0+2*k_7<=1+deltaext^0+wntext^0-k_7 ], cost: 4*k_7 75: l1 -> l1 : delta^0'=-k_10+delta^0, delta_new^0'=-k_10+delta^0, deltaext^0'=deltaext^0+k_10, deltaext_new^0'=deltaext^0+k_10, [ k_10>=1 && -1+2*deltaext^0+2*k_10<=2+wnt^0 && deltaext^0+wntext^0+k_10<=1-2*k_10+2*delta^0 ], cost: 4*k_10 76: 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 77: l1 -> l1 : delta^0'=delta^0-k_12, delta_new^0'=delta^0-k_12, deltaext^0'=deltaext^0-2*k_12, deltaext_new^0'=deltaext^0-2*k_12, [ 1+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=1+2*deltaext^0-4*k_12 ], cost: 8*k_12 78: l1 -> l1 : delta^0'=-1+delta^0-k_12, delta_new^0'=-1+delta^0-k_12, deltaext^0'=-1+deltaext^0-2*k_12, deltaext_new^0'=-1+deltaext^0-2*k_12, [ 3+wnt^0<=-1+2*deltaext^0 && 2+deltaext^0+wntext^0-2*delta^0==0 && k_12>=1 && 3+wnt^0<=-1+2*deltaext^0-4*k_12 ], cost: 4+8*k_12 79: l1 -> l1 : delta^0'=k_15+delta^0, delta_new^0'=k_15+delta^0, deltaext^0'=2*k_15+deltaext^0, deltaext_new^0'=2*k_15+deltaext^0, [ deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && -1+4*k_15+2*deltaext^0<=2+wnt^0 ], cost: 8*k_15 80: l1 -> l1 : delta^0'=1+k_15+delta^0, delta_new^0'=1+k_15+delta^0, deltaext^0'=1+2*k_15+deltaext^0, deltaext_new^0'=1+2*k_15+deltaext^0, [ 1+2*deltaext^0<=2+wnt^0 && -1+deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && 1+4*k_15+2*deltaext^0<=2+wnt^0 ], cost: 4+8*k_15 14: 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 14: 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 81: 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 82: 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 83: 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 84: 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 85: l6 -> [7] : [ 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^0-2*delta^0==0 ], cost: NONTERM 86: l6 -> [7] : [ 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 && deltaext^0+wntext^0-2*delta^0==0 ], cost: NONTERM 87: 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 88: l6 -> l1 : delta^0'=delta^0+k_1, delta_new^0'=delta^0+k_1, 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*delta^0+2*k_1<=deltaext^0+wntext^0 ], cost: 2+4*k_1 89: l6 -> [7] : [ 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^0-2*delta^0==0 ], cost: NONTERM 90: l6 -> [7] : [ 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 && deltaext^0+wntext^0-2*delta^0==0 ], cost: NONTERM 91: l6 -> l1 : delta^0'=delta^0-k_2, delta_new^0'=delta^0-k_2, 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*delta^0-2*k_2 ], cost: 2+4*k_2 92: l6 -> l1 : delta^0'=delta^0+k_3, delta_new^0'=delta^0+k_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 && k_3>=1 && -1+2*delta^0+2*k_3<=deltaext^0+wntext^0 ], cost: 2+4*k_3 93: l6 -> l1 : delta^0'=delta^0-k_6, delta_new^0'=delta^0-k_6, 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*delta^0-2*k_6 ], cost: 2+4*k_6 94: l6 -> l1 : delta^0'=delta^0+k_7, delta_new^0'=delta^0+k_7, deltaext^0'=deltaext^0-k_7, deltaext_new^0'=deltaext^0-k_7, [ 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*deltaext^0-2*k_7 && -1+2*delta^0+2*k_7<=1+deltaext^0+wntext^0-k_7 ], cost: 2+4*k_7 95: l6 -> l1 : delta^0'=-k_10+delta^0, delta_new^0'=-k_10+delta^0, deltaext^0'=deltaext^0+k_10, deltaext_new^0'=deltaext^0+k_10, [ 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*deltaext^0+2*k_10<=2+wnt^0 && deltaext^0+wntext^0+k_10<=1-2*k_10+2*delta^0 ], cost: 2+4*k_10 96: 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 97: l6 -> l1 : delta^0'=delta^0-k_12, delta_new^0'=delta^0-k_12, deltaext^0'=deltaext^0-2*k_12, deltaext_new^0'=deltaext^0-2*k_12, [ 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+2*deltaext^0-4*k_12 ], cost: 2+8*k_12 98: l6 -> l1 : delta^0'=-1+delta^0-k_12, delta_new^0'=-1+delta^0-k_12, deltaext^0'=-1+deltaext^0-2*k_12, deltaext_new^0'=-1+deltaext^0-2*k_12, [ 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+2*deltaext^0-4*k_12 ], cost: 6+8*k_12 99: l6 -> l1 : delta^0'=k_15+delta^0, delta_new^0'=k_15+delta^0, deltaext^0'=2*k_15+deltaext^0, deltaext_new^0'=2*k_15+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 && deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && -1+4*k_15+2*deltaext^0<=2+wnt^0 ], cost: 2+8*k_15 100: l6 -> l1 : delta^0'=1+k_15+delta^0, delta_new^0'=1+k_15+delta^0, deltaext^0'=1+2*k_15+deltaext^0, deltaext_new^0'=1+2*k_15+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 && k_15>=1 && 1+4*k_15+2*deltaext^0<=2+wnt^0 ], cost: 6+8*k_15 Removed unreachable locations (and leaf rules with constant cost): Start location: l6 85: l6 -> [7] : [ 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^0-2*delta^0==0 ], cost: NONTERM 86: l6 -> [7] : [ 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 && deltaext^0+wntext^0-2*delta^0==0 ], cost: NONTERM 87: 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 88: l6 -> l1 : delta^0'=delta^0+k_1, delta_new^0'=delta^0+k_1, 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*delta^0+2*k_1<=deltaext^0+wntext^0 ], cost: 2+4*k_1 89: l6 -> [7] : [ 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^0-2*delta^0==0 ], cost: NONTERM 90: l6 -> [7] : [ 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 && deltaext^0+wntext^0-2*delta^0==0 ], cost: NONTERM 91: l6 -> l1 : delta^0'=delta^0-k_2, delta_new^0'=delta^0-k_2, 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*delta^0-2*k_2 ], cost: 2+4*k_2 92: l6 -> l1 : delta^0'=delta^0+k_3, delta_new^0'=delta^0+k_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 && k_3>=1 && -1+2*delta^0+2*k_3<=deltaext^0+wntext^0 ], cost: 2+4*k_3 93: l6 -> l1 : delta^0'=delta^0-k_6, delta_new^0'=delta^0-k_6, 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*delta^0-2*k_6 ], cost: 2+4*k_6 94: l6 -> l1 : delta^0'=delta^0+k_7, delta_new^0'=delta^0+k_7, deltaext^0'=deltaext^0-k_7, deltaext_new^0'=deltaext^0-k_7, [ 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*deltaext^0-2*k_7 && -1+2*delta^0+2*k_7<=1+deltaext^0+wntext^0-k_7 ], cost: 2+4*k_7 95: l6 -> l1 : delta^0'=-k_10+delta^0, delta_new^0'=-k_10+delta^0, deltaext^0'=deltaext^0+k_10, deltaext_new^0'=deltaext^0+k_10, [ 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*deltaext^0+2*k_10<=2+wnt^0 && deltaext^0+wntext^0+k_10<=1-2*k_10+2*delta^0 ], cost: 2+4*k_10 96: 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 97: l6 -> l1 : delta^0'=delta^0-k_12, delta_new^0'=delta^0-k_12, deltaext^0'=deltaext^0-2*k_12, deltaext_new^0'=deltaext^0-2*k_12, [ 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+2*deltaext^0-4*k_12 ], cost: 2+8*k_12 98: l6 -> l1 : delta^0'=-1+delta^0-k_12, delta_new^0'=-1+delta^0-k_12, deltaext^0'=-1+deltaext^0-2*k_12, deltaext_new^0'=-1+deltaext^0-2*k_12, [ 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+2*deltaext^0-4*k_12 ], cost: 6+8*k_12 99: l6 -> l1 : delta^0'=k_15+delta^0, delta_new^0'=k_15+delta^0, deltaext^0'=2*k_15+deltaext^0, deltaext_new^0'=2*k_15+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 && deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && -1+4*k_15+2*deltaext^0<=2+wnt^0 ], cost: 2+8*k_15 100: l6 -> l1 : delta^0'=1+k_15+delta^0, delta_new^0'=1+k_15+delta^0, deltaext^0'=1+2*k_15+deltaext^0, deltaext_new^0'=1+2*k_15+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 && k_15>=1 && 1+4*k_15+2*deltaext^0<=2+wnt^0 ], cost: 6+8*k_15 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l6 85: l6 -> [7] : [ 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^0-2*delta^0==0 ], cost: NONTERM 86: l6 -> [7] : [ 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 && deltaext^0+wntext^0-2*delta^0==0 ], cost: NONTERM 87: 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 88: l6 -> l1 : delta^0'=delta^0+k_1, delta_new^0'=delta^0+k_1, 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*delta^0+2*k_1<=deltaext^0+wntext^0 ], cost: 2+4*k_1 89: l6 -> [7] : [ 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^0-2*delta^0==0 ], cost: NONTERM 90: l6 -> [7] : [ 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 && deltaext^0+wntext^0-2*delta^0==0 ], cost: NONTERM 91: l6 -> l1 : delta^0'=delta^0-k_2, delta_new^0'=delta^0-k_2, 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*delta^0-2*k_2 ], cost: 2+4*k_2 92: l6 -> l1 : delta^0'=delta^0+k_3, delta_new^0'=delta^0+k_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 && k_3>=1 && -1+2*delta^0+2*k_3<=deltaext^0+wntext^0 ], cost: 2+4*k_3 93: l6 -> l1 : delta^0'=delta^0-k_6, delta_new^0'=delta^0-k_6, 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*delta^0-2*k_6 ], cost: 2+4*k_6 94: l6 -> l1 : delta^0'=delta^0+k_7, delta_new^0'=delta^0+k_7, deltaext^0'=deltaext^0-k_7, deltaext_new^0'=deltaext^0-k_7, [ 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*deltaext^0-2*k_7 && -1+2*delta^0+2*k_7<=1+deltaext^0+wntext^0-k_7 ], cost: 2+4*k_7 95: l6 -> l1 : delta^0'=-k_10+delta^0, delta_new^0'=-k_10+delta^0, deltaext^0'=deltaext^0+k_10, deltaext_new^0'=deltaext^0+k_10, [ 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*deltaext^0+2*k_10<=2+wnt^0 && deltaext^0+wntext^0+k_10<=1-2*k_10+2*delta^0 ], cost: 2+4*k_10 96: 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 97: l6 -> l1 : delta^0'=delta^0-k_12, delta_new^0'=delta^0-k_12, deltaext^0'=deltaext^0-2*k_12, deltaext_new^0'=deltaext^0-2*k_12, [ 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+2*deltaext^0-4*k_12 ], cost: 2+8*k_12 98: l6 -> l1 : delta^0'=-1+delta^0-k_12, delta_new^0'=-1+delta^0-k_12, deltaext^0'=-1+deltaext^0-2*k_12, deltaext_new^0'=-1+deltaext^0-2*k_12, [ 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+2*deltaext^0-4*k_12 ], cost: 6+8*k_12 99: l6 -> l1 : delta^0'=k_15+delta^0, delta_new^0'=k_15+delta^0, deltaext^0'=2*k_15+deltaext^0, deltaext_new^0'=2*k_15+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 && deltaext^0+wntext^0-2*delta^0==0 && k_15>=1 && -1+4*k_15+2*deltaext^0<=2+wnt^0 ], cost: 2+8*k_15 100: l6 -> l1 : delta^0'=1+k_15+delta^0, delta_new^0'=1+k_15+delta^0, deltaext^0'=1+2*k_15+deltaext^0, deltaext_new^0'=1+2*k_15+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 && k_15>=1 && 1+4*k_15+2*deltaext^0<=2+wnt^0 ], cost: 6+8*k_15 Computing asymptotic complexity for rule 85 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: [ 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^0-2*delta^0==0 ] NO