YES Input TRS: 1: active(from(X)) -> mark(cons(X,from(s(X)))) 2: active(2ndspos(0(),Z)) -> mark(rnil()) 3: active(2ndspos(s(N),cons(X,cons(Y,Z)))) -> mark(rcons(posrecip(Y),2ndsneg(N,Z))) 4: active(2ndsneg(0(),Z)) -> mark(rnil()) 5: active(2ndsneg(s(N),cons(X,cons(Y,Z)))) -> mark(rcons(negrecip(Y),2ndspos(N,Z))) 6: active(pi(X)) -> mark(2ndspos(X,from(0()))) 7: active(plus(0(),Y)) -> mark(Y) 8: active(plus(s(X),Y)) -> mark(s(plus(X,Y))) 9: active(times(0(),Y)) -> mark(0()) 10: active(times(s(X),Y)) -> mark(plus(Y,times(X,Y))) 11: active(square(X)) -> mark(times(X,X)) 12: active(s(X)) -> s(active(X)) 13: active(posrecip(X)) -> posrecip(active(X)) 14: active(negrecip(X)) -> negrecip(active(X)) 15: active(cons(X1,X2)) -> cons(active(X1),X2) 16: active(rcons(X1,X2)) -> rcons(active(X1),X2) 17: active(rcons(X1,X2)) -> rcons(X1,active(X2)) 18: active(from(X)) -> from(active(X)) 19: active(2ndspos(X1,X2)) -> 2ndspos(active(X1),X2) 20: active(2ndspos(X1,X2)) -> 2ndspos(X1,active(X2)) 21: active(2ndsneg(X1,X2)) -> 2ndsneg(active(X1),X2) 22: active(2ndsneg(X1,X2)) -> 2ndsneg(X1,active(X2)) 23: active(pi(X)) -> pi(active(X)) 24: active(plus(X1,X2)) -> plus(active(X1),X2) 25: active(plus(X1,X2)) -> plus(X1,active(X2)) 26: active(times(X1,X2)) -> times(active(X1),X2) 27: active(times(X1,X2)) -> times(X1,active(X2)) 28: active(square(X)) -> square(active(X)) 29: s(mark(X)) -> mark(s(X)) 30: posrecip(mark(X)) -> mark(posrecip(X)) 31: negrecip(mark(X)) -> mark(negrecip(X)) 32: cons(mark(X1),X2) -> mark(cons(X1,X2)) 33: rcons(mark(X1),X2) -> mark(rcons(X1,X2)) 34: rcons(X1,mark(X2)) -> mark(rcons(X1,X2)) 35: from(mark(X)) -> mark(from(X)) 36: 2ndspos(mark(X1),X2) -> mark(2ndspos(X1,X2)) 37: 2ndspos(X1,mark(X2)) -> mark(2ndspos(X1,X2)) 38: 2ndsneg(mark(X1),X2) -> mark(2ndsneg(X1,X2)) 39: 2ndsneg(X1,mark(X2)) -> mark(2ndsneg(X1,X2)) 40: pi(mark(X)) -> mark(pi(X)) 41: plus(mark(X1),X2) -> mark(plus(X1,X2)) 42: plus(X1,mark(X2)) -> mark(plus(X1,X2)) 43: times(mark(X1),X2) -> mark(times(X1,X2)) 44: times(X1,mark(X2)) -> mark(times(X1,X2)) 45: square(mark(X)) -> mark(square(X)) 46: proper(0()) -> ok(0()) 47: proper(s(X)) -> s(proper(X)) 48: proper(posrecip(X)) -> posrecip(proper(X)) 49: proper(negrecip(X)) -> negrecip(proper(X)) 50: proper(nil()) -> ok(nil()) 51: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 52: proper(rnil()) -> ok(rnil()) 53: proper(rcons(X1,X2)) -> rcons(proper(X1),proper(X2)) 54: proper(from(X)) -> from(proper(X)) 55: proper(2ndspos(X1,X2)) -> 2ndspos(proper(X1),proper(X2)) 56: proper(2ndsneg(X1,X2)) -> 2ndsneg(proper(X1),proper(X2)) 57: proper(pi(X)) -> pi(proper(X)) 58: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) 59: proper(times(X1,X2)) -> times(proper(X1),proper(X2)) 60: proper(square(X)) -> square(proper(X)) 61: s(ok(X)) -> ok(s(X)) 62: posrecip(ok(X)) -> ok(posrecip(X)) 63: negrecip(ok(X)) -> ok(negrecip(X)) 64: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 65: rcons(ok(X1),ok(X2)) -> ok(rcons(X1,X2)) 66: from(ok(X)) -> ok(from(X)) 67: 2ndspos(ok(X1),ok(X2)) -> ok(2ndspos(X1,X2)) 68: 2ndsneg(ok(X1),ok(X2)) -> ok(2ndsneg(X1,X2)) 69: pi(ok(X)) -> ok(pi(X)) 70: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) 71: times(ok(X1),ok(X2)) -> ok(times(X1,X2)) 72: square(ok(X)) -> ok(square(X)) 73: top(mark(X)) -> top(proper(X)) 74: top(ok(X)) -> top(active(X)) Number of strict rules: 74 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #times(mark(X1),X2) -> #times(X1,X2) #2: #s(mark(X)) -> #s(X) #3: #from(mark(X)) -> #from(X) #4: #from(ok(X)) -> #from(X) #5: #plus(X1,mark(X2)) -> #plus(X1,X2) #6: #plus(mark(X1),X2) -> #plus(X1,X2) #7: #2ndspos(X1,mark(X2)) -> #2ndspos(X1,X2) #8: #top(mark(X)) -> #top(proper(X)) #9: #top(mark(X)) -> #proper(X) #10: #proper(s(X)) -> #s(proper(X)) #11: #proper(s(X)) -> #proper(X) #12: #proper(rcons(X1,X2)) -> #rcons(proper(X1),proper(X2)) #13: #proper(rcons(X1,X2)) -> #proper(X1) #14: #proper(rcons(X1,X2)) -> #proper(X2) #15: #times(ok(X1),ok(X2)) -> #times(X1,X2) #16: #proper(posrecip(X)) -> #posrecip(proper(X)) #17: #proper(posrecip(X)) -> #proper(X) #18: #top(ok(X)) -> #top(active(X)) #19: #top(ok(X)) -> #active(X) #20: #proper(plus(X1,X2)) -> #plus(proper(X1),proper(X2)) #21: #proper(plus(X1,X2)) -> #proper(X1) #22: #proper(plus(X1,X2)) -> #proper(X2) #23: #s(ok(X)) -> #s(X) #24: #2ndsneg(mark(X1),X2) -> #2ndsneg(X1,X2) #25: #active(pi(X)) -> #2ndspos(X,from(0())) #26: #active(pi(X)) -> #from(0()) #27: #proper(times(X1,X2)) -> #times(proper(X1),proper(X2)) #28: #proper(times(X1,X2)) -> #proper(X1) #29: #proper(times(X1,X2)) -> #proper(X2) #30: #proper(2ndspos(X1,X2)) -> #2ndspos(proper(X1),proper(X2)) #31: #proper(2ndspos(X1,X2)) -> #proper(X1) #32: #proper(2ndspos(X1,X2)) -> #proper(X2) #33: #2ndspos(ok(X1),ok(X2)) -> #2ndspos(X1,X2) #34: #pi(mark(X)) -> #pi(X) #35: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2)) #36: #proper(cons(X1,X2)) -> #proper(X1) #37: #proper(cons(X1,X2)) -> #proper(X2) #38: #active(posrecip(X)) -> #posrecip(active(X)) #39: #active(posrecip(X)) -> #active(X) #40: #active(square(X)) -> #times(X,X) #41: #proper(pi(X)) -> #pi(proper(X)) #42: #proper(pi(X)) -> #proper(X) #43: #active(plus(X1,X2)) -> #plus(active(X1),X2) #44: #active(plus(X1,X2)) -> #active(X1) #45: #plus(ok(X1),ok(X2)) -> #plus(X1,X2) #46: #active(pi(X)) -> #pi(active(X)) #47: #active(pi(X)) -> #active(X) #48: #square(mark(X)) -> #square(X) #49: #pi(ok(X)) -> #pi(X) #50: #active(s(X)) -> #s(active(X)) #51: #active(s(X)) -> #active(X) #52: #negrecip(mark(X)) -> #negrecip(X) #53: #proper(2ndsneg(X1,X2)) -> #2ndsneg(proper(X1),proper(X2)) #54: #proper(2ndsneg(X1,X2)) -> #proper(X1) #55: #proper(2ndsneg(X1,X2)) -> #proper(X2) #56: #active(negrecip(X)) -> #negrecip(active(X)) #57: #active(negrecip(X)) -> #active(X) #58: #posrecip(ok(X)) -> #posrecip(X) #59: #posrecip(mark(X)) -> #posrecip(X) #60: #proper(negrecip(X)) -> #negrecip(proper(X)) #61: #proper(negrecip(X)) -> #proper(X) #62: #active(plus(X1,X2)) -> #plus(X1,active(X2)) #63: #active(plus(X1,X2)) -> #active(X2) #64: #active(2ndspos(X1,X2)) -> #2ndspos(X1,active(X2)) #65: #active(2ndspos(X1,X2)) -> #active(X2) #66: #2ndsneg(X1,mark(X2)) -> #2ndsneg(X1,X2) #67: #active(times(s(X),Y)) -> #plus(Y,times(X,Y)) #68: #active(times(s(X),Y)) -> #times(X,Y) #69: #cons(ok(X1),ok(X2)) -> #cons(X1,X2) #70: #rcons(mark(X1),X2) -> #rcons(X1,X2) #71: #square(ok(X)) -> #square(X) #72: #active(2ndsneg(s(N),cons(X,cons(Y,Z)))) -> #rcons(negrecip(Y),2ndspos(N,Z)) #73: #active(2ndsneg(s(N),cons(X,cons(Y,Z)))) -> #negrecip(Y) #74: #active(2ndsneg(s(N),cons(X,cons(Y,Z)))) -> #2ndspos(N,Z) #75: #times(X1,mark(X2)) -> #times(X1,X2) #76: #rcons(ok(X1),ok(X2)) -> #rcons(X1,X2) #77: #active(square(X)) -> #square(active(X)) #78: #active(square(X)) -> #active(X) #79: #active(2ndsneg(X1,X2)) -> #2ndsneg(X1,active(X2)) #80: #active(2ndsneg(X1,X2)) -> #active(X2) #81: #rcons(X1,mark(X2)) -> #rcons(X1,X2) #82: #active(times(X1,X2)) -> #times(X1,active(X2)) #83: #active(times(X1,X2)) -> #active(X2) #84: #proper(square(X)) -> #square(proper(X)) #85: #proper(square(X)) -> #proper(X) #86: #active(rcons(X1,X2)) -> #rcons(X1,active(X2)) #87: #active(rcons(X1,X2)) -> #active(X2) #88: #cons(mark(X1),X2) -> #cons(X1,X2) #89: #active(2ndspos(X1,X2)) -> #2ndspos(active(X1),X2) #90: #active(2ndspos(X1,X2)) -> #active(X1) #91: #negrecip(ok(X)) -> #negrecip(X) #92: #active(times(X1,X2)) -> #times(active(X1),X2) #93: #active(times(X1,X2)) -> #active(X1) #94: #2ndsneg(ok(X1),ok(X2)) -> #2ndsneg(X1,X2) #95: #2ndspos(mark(X1),X2) -> #2ndspos(X1,X2) #96: #active(2ndsneg(X1,X2)) -> #2ndsneg(active(X1),X2) #97: #active(2ndsneg(X1,X2)) -> #active(X1) #98: #active(rcons(X1,X2)) -> #rcons(active(X1),X2) #99: #active(rcons(X1,X2)) -> #active(X1) #100: #active(2ndspos(s(N),cons(X,cons(Y,Z)))) -> #rcons(posrecip(Y),2ndsneg(N,Z)) #101: #active(2ndspos(s(N),cons(X,cons(Y,Z)))) -> #posrecip(Y) #102: #active(2ndspos(s(N),cons(X,cons(Y,Z)))) -> #2ndsneg(N,Z) #103: #active(from(X)) -> #cons(X,from(s(X))) #104: #active(from(X)) -> #from(s(X)) #105: #active(from(X)) -> #s(X) #106: #proper(from(X)) -> #from(proper(X)) #107: #proper(from(X)) -> #proper(X) #108: #active(plus(s(X),Y)) -> #s(plus(X,Y)) #109: #active(plus(s(X),Y)) -> #plus(X,Y) #110: #active(cons(X1,X2)) -> #cons(active(X1),X2) #111: #active(cons(X1,X2)) -> #active(X1) #112: #active(from(X)) -> #from(active(X)) #113: #active(from(X)) -> #active(X) Number of SCCs: 15, DPs: 66 SCC { #58 #59 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 top w: 0 rnil w: 0 #plus w: 0 square w: 0 #top w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 proper w: 0 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: x1 from w: 0 times w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 2ndsneg w: 0 #proper w: 0 plus w: 0 #2ndspos w: 0 #from w: 0 active w: 0 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #58 #59 Number of SCCs: 14, DPs: 64 SCC { #34 #49 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 top w: 0 rnil w: 0 #plus w: 0 square w: 0 #top w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 proper w: 0 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 2ndsneg w: 0 #proper w: 0 plus w: 0 #2ndspos w: 0 #from w: 0 active w: 0 cons w: 0 #active w: 0 #pi w: x1 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #34 #49 Number of SCCs: 13, DPs: 62 SCC { #52 #91 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: x1 2ndspos w: 0 top w: 0 rnil w: 0 #plus w: 0 square w: 0 #top w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 proper w: 0 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 2ndsneg w: 0 #proper w: 0 plus w: 0 #2ndspos w: 0 #from w: 0 active w: 0 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #52 #91 Number of SCCs: 12, DPs: 60 SCC { #48 #71 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 top w: 0 rnil w: 0 #plus w: 0 square w: 0 #top w: 0 #square w: x1 pi w: 0 #rcons w: 0 rcons w: 0 proper w: 0 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 2ndsneg w: 0 #proper w: 0 plus w: 0 #2ndspos w: 0 #from w: 0 active w: 0 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #48 #71 Number of SCCs: 11, DPs: 58 SCC { #3 #4 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 top w: 0 rnil w: 0 #plus w: 0 square w: 0 #top w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 proper w: 0 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 2ndsneg w: 0 #proper w: 0 plus w: 0 #2ndspos w: 0 #from w: x1 active w: 0 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #3 #4 Number of SCCs: 10, DPs: 56 SCC { #2 #23 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 top w: 0 rnil w: 0 #plus w: 0 square w: 0 #top w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 proper w: 0 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: x1 nil w: 0 mark w: x1 + 1 2ndsneg w: 0 #proper w: 0 plus w: 0 #2ndspos w: 0 #from w: 0 active w: 0 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #2 #23 Number of SCCs: 9, DPs: 54 SCC { #8 #18 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. negrecip s: [1] p: 3 w: x1 + 3 #cons s: [1] p: 0 w: max(x1 + 1) s s: [1] p: 1 w: x1 #negrecip s: [] p: 0 w: 1 2ndspos s: [1,2] p: 5 w: x1 + x2 + 23616 top s: [] p: 0 w: 1 rnil s: [] p: 5 w: 1 #plus s: [2,1] p: 0 w: max(x1 + 1, x2 + 1) square s: [1] p: 5 w: x1 + 21242 #top s: 1 #square s: [] p: 0 w: 1 pi s: [1] p: 6 w: x1 + 47235 #rcons s: [1] p: 0 w: max(x1 + 1) rcons s: [2,1] p: 3 w: max(x1 + 23614, x2) proper s: 1 ok s: 1 #times s: [] p: 0 w: max(x1 + 1) 0 s: [] p: 7 w: 2 #posrecip s: 1 from s: [1] p: 5 w: x1 + 23616 times s: [2,1] p: 3 w: max(x1 + 21241, x2 + 21240) #s s: [] p: 0 w: 1 nil s: [] p: 6 w: 25074 mark s: [1] p: 0 w: x1 2ndsneg s: [1,2] p: 5 w: x1 + x2 + 23616 #proper s: [] p: 0 w: 1 plus s: [1,2] p: 2 w: max(x1 + 21240, x2) #2ndspos s: [2,1] p: 0 w: x1 + x2 + 1 #from s: [] p: 0 w: 1 active s: 1 cons s: [1] p: 4 w: max(x1 + 23615, x2) #active s: [] p: 0 w: 1 #pi s: [] p: 0 w: 1 #2ndsneg s: [] p: 0 w: 1 posrecip s: [1] p: 3 w: x1 + 23617 USABLE RULES: { 1..72 } Removed DPs: #8 Number of SCCs: 9, DPs: 53 SCC { #18 } POLO(Sum)... succeeded. negrecip w: x1 #cons w: 0 s w: x1 #negrecip w: 0 2ndspos w: x1 top w: 0 rnil w: 1 #plus w: 0 square w: x1 #top w: x1 #square w: 0 pi w: x1 #rcons w: 0 rcons w: x1 proper w: 15013 ok w: x1 + 2 #times w: 0 0 w: 15011 #posrecip w: 0 from w: x1 times w: x2 #s w: 0 nil w: 840 mark w: 0 2ndsneg w: x2 #proper w: 0 plus w: x2 #2ndspos w: 0 #from w: 0 active w: x1 + 1 cons w: x1 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 USABLE RULES: { 1..72 } Removed DPs: #18 Number of SCCs: 8, DPs: 52 SCC { #69 #88 } POLO(Sum)... succeeded. negrecip w: x1 #cons w: x2 s w: x1 #negrecip w: 0 2ndspos w: x1 top w: 0 rnil w: 1 #plus w: 0 square w: x1 #top w: x1 #square w: 0 pi w: x1 #rcons w: 0 rcons w: x1 proper w: 2 ok w: x1 + 1 #times w: 0 0 w: 1 #posrecip w: 0 from w: x1 times w: x2 #s w: 0 nil w: 1 mark w: 0 2ndsneg w: x2 #proper w: 0 plus w: x2 #2ndspos w: 0 #from w: 0 active w: x1 + 1 cons w: x1 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 USABLE RULES: { 1..72 } Removed DPs: #69 Number of SCCs: 8, DPs: 51 SCC { #88 } POLO(Sum)... succeeded. negrecip w: x1 #cons w: x1 s w: x1 #negrecip w: 0 2ndspos w: x1 top w: 0 rnil w: 1 #plus w: 0 square w: x1 #top w: 0 #square w: 0 pi w: x1 #rcons w: 0 rcons w: x1 + x2 proper w: 1 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: x1 times w: 0 #s w: 0 nil w: 1 mark w: x1 + 1 2ndsneg w: x1 + x2 #proper w: 0 plus w: x2 #2ndspos w: 0 #from w: 0 active w: x1 + 2 cons w: x1 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 USABLE RULES: { 2 4 7 9 38 39 68 } Removed DPs: #88 Number of SCCs: 7, DPs: 50 SCC { #1 #15 #75 } POLO(Sum)... succeeded. negrecip w: x1 #cons w: 0 s w: x1 #negrecip w: 0 2ndspos w: x1 top w: 0 rnil w: 2 #plus w: 0 square w: x1 #top w: 0 #square w: 0 pi w: x1 #rcons w: 0 rcons w: x1 + x2 proper w: 1 ok w: x1 + 1 #times w: x2 0 w: 0 #posrecip w: 0 from w: x1 times w: 0 #s w: 0 nil w: 1 mark w: x1 + 1 2ndsneg w: x1 + x2 #proper w: 0 plus w: x2 #2ndspos w: 0 #from w: 0 active w: x1 + 3 cons w: x1 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 USABLE RULES: { 2 4 7 9 38 39 68 } Removed DPs: #15 #75 Number of SCCs: 7, DPs: 48 SCC { #1 } POLO(Sum)... succeeded. negrecip w: x1 #cons w: 0 s w: x1 #negrecip w: 0 2ndspos w: x1 top w: 0 rnil w: 1 #plus w: 0 square w: x1 #top w: 0 #square w: 0 pi w: x1 #rcons w: 0 rcons w: x1 + x2 proper w: 1 ok w: x1 + 1 #times w: x1 0 w: 0 #posrecip w: 0 from w: x1 times w: 0 #s w: 0 nil w: 1 mark w: x1 + 1 2ndsneg w: x1 + x2 #proper w: 0 plus w: x2 #2ndspos w: 0 #from w: 0 active w: x1 + 2 cons w: x1 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 USABLE RULES: { 2 4 7 9 38 39 68 } Removed DPs: #1 Number of SCCs: 6, DPs: 47 SCC { #7 #33 #95 } POLO(Sum)... succeeded. negrecip w: x1 #cons w: 0 s w: x1 #negrecip w: 0 2ndspos w: x1 top w: 0 rnil w: 1 #plus w: 0 square w: x1 #top w: 0 #square w: 0 pi w: x1 #rcons w: 0 rcons w: x1 + x2 proper w: 1 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: x1 times w: 0 #s w: 0 nil w: 1 mark w: x1 + 1 2ndsneg w: x1 + x2 #proper w: 0 plus w: x2 #2ndspos w: x1 #from w: 0 active w: x1 + 2 cons w: x1 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 USABLE RULES: { 2 4 7 9 38 39 68 } Removed DPs: #33 #95 Number of SCCs: 6, DPs: 45 SCC { #7 } POLO(Sum)... succeeded. negrecip w: x1 #cons w: 0 s w: x1 #negrecip w: 0 2ndspos w: x1 top w: 0 rnil w: 1 #plus w: 0 square w: x1 #top w: 0 #square w: 0 pi w: x1 #rcons w: 0 rcons w: x1 + x2 proper w: 1 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: x1 times w: 0 #s w: 0 nil w: 1 mark w: x1 + 1 2ndsneg w: x1 + x2 #proper w: 0 plus w: x2 #2ndspos w: x2 #from w: 0 active w: x1 + 2 cons w: x1 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 USABLE RULES: { 2 4 7 9 38 39 68 } Removed DPs: #7 Number of SCCs: 5, DPs: 44 SCC { #24 #66 #94 } POLO(Sum)... succeeded. negrecip w: x1 #cons w: 0 s w: x1 #negrecip w: 0 2ndspos w: x1 top w: 0 rnil w: 2 #plus w: 0 square w: x1 #top w: 0 #square w: 0 pi w: x1 #rcons w: 0 rcons w: x1 + x2 proper w: 1 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: x1 times w: 0 #s w: 0 nil w: 1 mark w: x1 + 1 2ndsneg w: x1 + x2 #proper w: 0 plus w: x2 #2ndspos w: 0 #from w: 0 active w: x1 + 3 cons w: x1 #active w: 0 #pi w: 0 #2ndsneg w: x1 + x2 posrecip w: x1 USABLE RULES: { 2 4 7 9 38 39 68 } Removed DPs: #24 #66 #94 Number of SCCs: 4, DPs: 41 SCC { #70 #76 #81 } POLO(Sum)... succeeded. negrecip w: x1 #cons w: 0 s w: x1 #negrecip w: 0 2ndspos w: x1 top w: 0 rnil w: 1 #plus w: 0 square w: x1 #top w: 0 #square w: 0 pi w: x1 #rcons w: x1 + x2 rcons w: x1 + x2 proper w: 1 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: x1 times w: 0 #s w: 0 nil w: 1 mark w: x1 + 1 2ndsneg w: x1 + x2 #proper w: 0 plus w: x2 #2ndspos w: 0 #from w: 0 active w: x1 + 2 cons w: x1 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 USABLE RULES: { 2 4 7 9 38 39 68 } Removed DPs: #70 #76 #81 Number of SCCs: 3, DPs: 38 SCC { #5 #6 #45 } POLO(Sum)... succeeded. negrecip w: x1 #cons w: 0 s w: x1 #negrecip w: 0 2ndspos w: x1 top w: 0 rnil w: 1 #plus w: x1 + x2 square w: x1 #top w: 0 #square w: 0 pi w: x1 #rcons w: 0 rcons w: x1 + x2 proper w: 1 ok w: x1 + 1 #times w: 0 0 w: 0 #posrecip w: 0 from w: x1 times w: 0 #s w: 0 nil w: 1 mark w: x1 + 1 2ndsneg w: x1 + x2 #proper w: 0 plus w: x2 #2ndspos w: 0 #from w: 0 active w: x1 + 2 cons w: x1 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 USABLE RULES: { 2 4 7 9 38 39 68 } Removed DPs: #5 #6 #45 Number of SCCs: 2, DPs: 35 SCC { #39 #44 #47 #51 #57 #63 #65 #78 #80 #83 #87 #90 #93 #97 #99 #111 #113 } POLO(Sum)... succeeded. negrecip w: x1 + 1 #cons w: 0 s w: x1 + 2 #negrecip w: 0 2ndspos w: x1 + x2 + 1 top w: 0 rnil w: 1 #plus w: 0 square w: x1 + 13856 #top w: 0 #square w: 0 pi w: x1 + 5 #rcons w: 0 rcons w: x1 + x2 + 1 proper w: x1 + 1 ok w: 3 #times w: 0 0 w: 2 #posrecip w: 0 from w: x1 + 1 times w: x1 + x2 + 1 #s w: 0 nil w: 1 mark w: x1 + 1 2ndsneg w: x1 + x2 + 1 #proper w: 0 plus w: x1 + x2 + 1 #2ndspos w: 0 #from w: 0 active w: x1 cons w: x1 + x2 + 1 #active w: x1 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 + 1 USABLE RULES: { 2 4 9 38 39 68 } Removed DPs: #39 #44 #47 #51 #57 #63 #65 #78 #80 #83 #87 #90 #93 #97 #99 #111 #113 Number of SCCs: 1, DPs: 18 SCC { #11 #13 #14 #17 #21 #22 #28 #29 #31 #32 #36 #37 #42 #54 #55 #61 #85 #107 } POLO(Sum)... succeeded. negrecip w: x1 + 1 #cons w: 0 s w: x1 + 7363 #negrecip w: 0 2ndspos w: x1 + x2 + 1 top w: 0 rnil w: 1 #plus w: 0 square w: x1 + 33769 #top w: 0 #square w: 0 pi w: x1 + 5 #rcons w: 0 rcons w: x1 + x2 + 7363 proper w: x1 + 1 ok w: 3 #times w: 0 0 w: 2 #posrecip w: 0 from w: x1 + 1 times w: x1 + x2 + 33768 #s w: 0 nil w: 1 mark w: x1 + 1 2ndsneg w: x1 + x2 + 1 #proper w: x1 plus w: x1 + x2 + 1 #2ndspos w: 0 #from w: 0 active w: x1 cons w: x1 + x2 + 1 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 + 1 USABLE RULES: { 2 4 9 38 39 68 } Removed DPs: #11 #13 #14 #17 #21 #22 #28 #29 #31 #32 #36 #37 #42 #54 #55 #61 #85 #107 Number of SCCs: 0, DPs: 0