/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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,Z))) -> mark(2ndspos(s(N),cons2(X,Z))) 4: active(2ndspos(s(N),cons2(X,cons(Y,Z)))) -> mark(rcons(posrecip(Y),2ndsneg(N,Z))) 5: active(2ndsneg(0(),Z)) -> mark(rnil()) 6: active(2ndsneg(s(N),cons(X,Z))) -> mark(2ndsneg(s(N),cons2(X,Z))) 7: active(2ndsneg(s(N),cons2(X,cons(Y,Z)))) -> mark(rcons(negrecip(Y),2ndspos(N,Z))) 8: active(pi(X)) -> mark(2ndspos(X,from(0()))) 9: active(plus(0(),Y)) -> mark(Y) 10: active(plus(s(X),Y)) -> mark(s(plus(X,Y))) 11: active(times(0(),Y)) -> mark(0()) 12: active(times(s(X),Y)) -> mark(plus(Y,times(X,Y))) 13: active(square(X)) -> mark(times(X,X)) 14: mark(from(X)) -> active(from(mark(X))) 15: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) 16: mark(s(X)) -> active(s(mark(X))) 17: mark(2ndspos(X1,X2)) -> active(2ndspos(mark(X1),mark(X2))) 18: mark(0()) -> active(0()) 19: mark(rnil()) -> active(rnil()) 20: mark(cons2(X1,X2)) -> active(cons2(X1,mark(X2))) 21: mark(rcons(X1,X2)) -> active(rcons(mark(X1),mark(X2))) 22: mark(posrecip(X)) -> active(posrecip(mark(X))) 23: mark(2ndsneg(X1,X2)) -> active(2ndsneg(mark(X1),mark(X2))) 24: mark(negrecip(X)) -> active(negrecip(mark(X))) 25: mark(pi(X)) -> active(pi(mark(X))) 26: mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 27: mark(times(X1,X2)) -> active(times(mark(X1),mark(X2))) 28: mark(square(X)) -> active(square(mark(X))) 29: from(mark(X)) -> from(X) 30: from(active(X)) -> from(X) 31: cons(mark(X1),X2) -> cons(X1,X2) 32: cons(X1,mark(X2)) -> cons(X1,X2) 33: cons(active(X1),X2) -> cons(X1,X2) 34: cons(X1,active(X2)) -> cons(X1,X2) 35: s(mark(X)) -> s(X) 36: s(active(X)) -> s(X) 37: 2ndspos(mark(X1),X2) -> 2ndspos(X1,X2) 38: 2ndspos(X1,mark(X2)) -> 2ndspos(X1,X2) 39: 2ndspos(active(X1),X2) -> 2ndspos(X1,X2) 40: 2ndspos(X1,active(X2)) -> 2ndspos(X1,X2) 41: cons2(mark(X1),X2) -> cons2(X1,X2) 42: cons2(X1,mark(X2)) -> cons2(X1,X2) 43: cons2(active(X1),X2) -> cons2(X1,X2) 44: cons2(X1,active(X2)) -> cons2(X1,X2) 45: rcons(mark(X1),X2) -> rcons(X1,X2) 46: rcons(X1,mark(X2)) -> rcons(X1,X2) 47: rcons(active(X1),X2) -> rcons(X1,X2) 48: rcons(X1,active(X2)) -> rcons(X1,X2) 49: posrecip(mark(X)) -> posrecip(X) 50: posrecip(active(X)) -> posrecip(X) 51: 2ndsneg(mark(X1),X2) -> 2ndsneg(X1,X2) 52: 2ndsneg(X1,mark(X2)) -> 2ndsneg(X1,X2) 53: 2ndsneg(active(X1),X2) -> 2ndsneg(X1,X2) 54: 2ndsneg(X1,active(X2)) -> 2ndsneg(X1,X2) 55: negrecip(mark(X)) -> negrecip(X) 56: negrecip(active(X)) -> negrecip(X) 57: pi(mark(X)) -> pi(X) 58: pi(active(X)) -> pi(X) 59: plus(mark(X1),X2) -> plus(X1,X2) 60: plus(X1,mark(X2)) -> plus(X1,X2) 61: plus(active(X1),X2) -> plus(X1,X2) 62: plus(X1,active(X2)) -> plus(X1,X2) 63: times(mark(X1),X2) -> times(X1,X2) 64: times(X1,mark(X2)) -> times(X1,X2) 65: times(active(X1),X2) -> times(X1,X2) 66: times(X1,active(X2)) -> times(X1,X2) 67: square(mark(X)) -> square(X) 68: square(active(X)) -> square(X) Number of strict rules: 68 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #active(2ndspos(0(),Z)) -> #mark(rnil()) #2: #cons2(active(X1),X2) -> #cons2(X1,X2) #3: #from(mark(X)) -> #from(X) #4: #s(mark(X)) -> #s(X) #5: #times(X1,active(X2)) -> #times(X1,X2) #6: #rcons(X1,mark(X2)) -> #rcons(X1,X2) #7: #cons2(X1,mark(X2)) -> #cons2(X1,X2) #8: #cons2(mark(X1),X2) -> #cons2(X1,X2) #9: #2ndspos(mark(X1),X2) -> #2ndspos(X1,X2) #10: #rcons(active(X1),X2) -> #rcons(X1,X2) #11: #2ndsneg(active(X1),X2) -> #2ndsneg(X1,X2) #12: #rcons(X1,active(X2)) -> #rcons(X1,X2) #13: #pi(active(X)) -> #pi(X) #14: #plus(active(X1),X2) -> #plus(X1,X2) #15: #2ndspos(X1,mark(X2)) -> #2ndspos(X1,X2) #16: #active(2ndsneg(s(N),cons(X,Z))) -> #mark(2ndsneg(s(N),cons2(X,Z))) #17: #active(2ndsneg(s(N),cons(X,Z))) -> #2ndsneg(s(N),cons2(X,Z)) #18: #active(2ndsneg(s(N),cons(X,Z))) -> #cons2(X,Z) #19: #plus(mark(X1),X2) -> #plus(X1,X2) #20: #negrecip(mark(X)) -> #negrecip(X) #21: #square(mark(X)) -> #square(X) #22: #2ndspos(X1,active(X2)) -> #2ndspos(X1,X2) #23: #2ndsneg(mark(X1),X2) -> #2ndsneg(X1,X2) #24: #active(square(X)) -> #mark(times(X,X)) #25: #active(square(X)) -> #times(X,X) #26: #active(plus(0(),Y)) -> #mark(Y) #27: #active(times(0(),Y)) -> #mark(0()) #28: #pi(mark(X)) -> #pi(X) #29: #mark(negrecip(X)) -> #active(negrecip(mark(X))) #30: #mark(negrecip(X)) -> #negrecip(mark(X)) #31: #mark(negrecip(X)) -> #mark(X) #32: #mark(2ndsneg(X1,X2)) -> #active(2ndsneg(mark(X1),mark(X2))) #33: #mark(2ndsneg(X1,X2)) -> #2ndsneg(mark(X1),mark(X2)) #34: #mark(2ndsneg(X1,X2)) -> #mark(X1) #35: #mark(2ndsneg(X1,X2)) -> #mark(X2) #36: #rcons(mark(X1),X2) -> #rcons(X1,X2) #37: #active(times(s(X),Y)) -> #mark(plus(Y,times(X,Y))) #38: #active(times(s(X),Y)) -> #plus(Y,times(X,Y)) #39: #active(times(s(X),Y)) -> #times(X,Y) #40: #cons(mark(X1),X2) -> #cons(X1,X2) #41: #negrecip(active(X)) -> #negrecip(X) #42: #mark(from(X)) -> #active(from(mark(X))) #43: #mark(from(X)) -> #from(mark(X)) #44: #mark(from(X)) -> #mark(X) #45: #plus(X1,active(X2)) -> #plus(X1,X2) #46: #from(active(X)) -> #from(X) #47: #2ndsneg(X1,mark(X2)) -> #2ndsneg(X1,X2) #48: #posrecip(mark(X)) -> #posrecip(X) #49: #mark(pi(X)) -> #active(pi(mark(X))) #50: #mark(pi(X)) -> #pi(mark(X)) #51: #mark(pi(X)) -> #mark(X) #52: #mark(cons2(X1,X2)) -> #active(cons2(X1,mark(X2))) #53: #mark(cons2(X1,X2)) -> #cons2(X1,mark(X2)) #54: #mark(cons2(X1,X2)) -> #mark(X2) #55: #active(2ndsneg(s(N),cons2(X,cons(Y,Z)))) -> #mark(rcons(negrecip(Y),2ndspos(N,Z))) #56: #active(2ndsneg(s(N),cons2(X,cons(Y,Z)))) -> #rcons(negrecip(Y),2ndspos(N,Z)) #57: #active(2ndsneg(s(N),cons2(X,cons(Y,Z)))) -> #negrecip(Y) #58: #active(2ndsneg(s(N),cons2(X,cons(Y,Z)))) -> #2ndspos(N,Z) #59: #2ndspos(active(X1),X2) -> #2ndspos(X1,X2) #60: #active(plus(s(X),Y)) -> #mark(s(plus(X,Y))) #61: #active(plus(s(X),Y)) -> #s(plus(X,Y)) #62: #active(plus(s(X),Y)) -> #plus(X,Y) #63: #times(X1,mark(X2)) -> #times(X1,X2) #64: #cons(active(X1),X2) -> #cons(X1,X2) #65: #active(2ndsneg(0(),Z)) -> #mark(rnil()) #66: #cons2(X1,active(X2)) -> #cons2(X1,X2) #67: #times(active(X1),X2) -> #times(X1,X2) #68: #mark(square(X)) -> #active(square(mark(X))) #69: #mark(square(X)) -> #square(mark(X)) #70: #mark(square(X)) -> #mark(X) #71: #mark(posrecip(X)) -> #active(posrecip(mark(X))) #72: #mark(posrecip(X)) -> #posrecip(mark(X)) #73: #mark(posrecip(X)) -> #mark(X) #74: #cons(X1,active(X2)) -> #cons(X1,X2) #75: #mark(times(X1,X2)) -> #active(times(mark(X1),mark(X2))) #76: #mark(times(X1,X2)) -> #times(mark(X1),mark(X2)) #77: #mark(times(X1,X2)) -> #mark(X1) #78: #mark(times(X1,X2)) -> #mark(X2) #79: #plus(X1,mark(X2)) -> #plus(X1,X2) #80: #mark(2ndspos(X1,X2)) -> #active(2ndspos(mark(X1),mark(X2))) #81: #mark(2ndspos(X1,X2)) -> #2ndspos(mark(X1),mark(X2)) #82: #mark(2ndspos(X1,X2)) -> #mark(X1) #83: #mark(2ndspos(X1,X2)) -> #mark(X2) #84: #cons(X1,mark(X2)) -> #cons(X1,X2) #85: #mark(rnil()) -> #active(rnil()) #86: #times(mark(X1),X2) -> #times(X1,X2) #87: #mark(plus(X1,X2)) -> #active(plus(mark(X1),mark(X2))) #88: #mark(plus(X1,X2)) -> #plus(mark(X1),mark(X2)) #89: #mark(plus(X1,X2)) -> #mark(X1) #90: #mark(plus(X1,X2)) -> #mark(X2) #91: #square(active(X)) -> #square(X) #92: #s(active(X)) -> #s(X) #93: #mark(rcons(X1,X2)) -> #active(rcons(mark(X1),mark(X2))) #94: #mark(rcons(X1,X2)) -> #rcons(mark(X1),mark(X2)) #95: #mark(rcons(X1,X2)) -> #mark(X1) #96: #mark(rcons(X1,X2)) -> #mark(X2) #97: #mark(s(X)) -> #active(s(mark(X))) #98: #mark(s(X)) -> #s(mark(X)) #99: #mark(s(X)) -> #mark(X) #100: #active(2ndspos(s(N),cons(X,Z))) -> #mark(2ndspos(s(N),cons2(X,Z))) #101: #active(2ndspos(s(N),cons(X,Z))) -> #2ndspos(s(N),cons2(X,Z)) #102: #active(2ndspos(s(N),cons(X,Z))) -> #cons2(X,Z) #103: #active(from(X)) -> #mark(cons(X,from(s(X)))) #104: #active(from(X)) -> #cons(X,from(s(X))) #105: #active(from(X)) -> #from(s(X)) #106: #active(from(X)) -> #s(X) #107: #2ndsneg(X1,active(X2)) -> #2ndsneg(X1,X2) #108: #active(pi(X)) -> #mark(2ndspos(X,from(0()))) #109: #active(pi(X)) -> #2ndspos(X,from(0())) #110: #active(pi(X)) -> #from(0()) #111: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2)) #112: #mark(cons(X1,X2)) -> #cons(mark(X1),X2) #113: #mark(cons(X1,X2)) -> #mark(X1) #114: #active(2ndspos(s(N),cons2(X,cons(Y,Z)))) -> #mark(rcons(posrecip(Y),2ndsneg(N,Z))) #115: #active(2ndspos(s(N),cons2(X,cons(Y,Z)))) -> #rcons(posrecip(Y),2ndsneg(N,Z)) #116: #active(2ndspos(s(N),cons2(X,cons(Y,Z)))) -> #posrecip(Y) #117: #active(2ndspos(s(N),cons2(X,cons(Y,Z)))) -> #2ndsneg(N,Z) #118: #posrecip(active(X)) -> #posrecip(X) #119: #mark(0()) -> #active(0()) Number of SCCs: 14, DPs: 75 SCC { #13 #28 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: x1 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #13 #28 Number of SCCs: 13, DPs: 73 SCC { #21 #91 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: x1 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #21 #91 Number of SCCs: 12, DPs: 71 SCC { #48 #118 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: x1 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #48 #118 Number of SCCs: 11, DPs: 69 SCC { #4 #92 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: x1 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #4 #92 Number of SCCs: 10, DPs: 67 SCC { #3 #46 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: x1 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #3 #46 Number of SCCs: 9, DPs: 65 SCC { #20 #41 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: x1 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #20 #41 Number of SCCs: 8, DPs: 63 SCC { #11 #23 #47 #107 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: x1 posrecip w: 0 USABLE RULES: { } Removed DPs: #11 #23 Number of SCCs: 8, DPs: 61 SCC { #47 #107 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: x2 posrecip w: 0 USABLE RULES: { } Removed DPs: #47 #107 Number of SCCs: 7, DPs: 59 SCC { #9 #15 #22 #59 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: x1 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #9 #59 Number of SCCs: 7, DPs: 57 SCC { #15 #22 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: x2 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #15 #22 Number of SCCs: 6, DPs: 55 SCC { #14 #19 #45 #79 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: x2 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #45 #79 Number of SCCs: 6, DPs: 53 SCC { #14 #19 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: x1 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #14 #19 Number of SCCs: 5, DPs: 51 SCC { #6 #10 #12 #36 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: x2 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #6 #12 Number of SCCs: 5, DPs: 49 SCC { #10 #36 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: x1 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #10 #36 Number of SCCs: 4, DPs: 47 SCC { #40 #64 #74 #84 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: x2 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #74 #84 Number of SCCs: 4, DPs: 45 SCC { #40 #64 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: x1 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #40 #64 Number of SCCs: 3, DPs: 43 SCC { #5 #63 #67 #86 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: x2 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #5 #63 Number of SCCs: 3, DPs: 41 SCC { #67 #86 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: 0 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: x1 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #67 #86 Number of SCCs: 2, DPs: 39 SCC { #2 #7 #8 #66 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: x2 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #7 #66 Number of SCCs: 2, DPs: 37 SCC { #2 #8 } POLO(Sum)... succeeded. negrecip w: 0 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: 0 rnil w: 0 #plus w: 0 square w: 0 #cons2 w: x1 #square w: 0 pi w: 0 #rcons w: 0 rcons w: 0 #times w: 0 #mark w: 0 0 w: 0 #posrecip w: 0 from w: 0 times w: 0 #s w: 0 mark w: x1 + 1 2ndsneg w: 0 plus w: 0 #2ndspos w: 0 cons2 w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #pi w: 0 #2ndsneg w: 0 posrecip w: 0 USABLE RULES: { } Removed DPs: #2 #8 Number of SCCs: 1, DPs: 35 SCC { #16 #24 #26 #31 #32 #34 #35 #37 #42 #44 #49 #51 #54 #55 #60 #68 #70 #73 #75 #77 #78 #80 #82 #83 #87 #89 #90 #95 #96 #99 #100 #103 #108 #113 #114 } POLO(Sum)... POLO(max)... succeeded. negrecip w: x1 + 1 #cons w: 0 s w: x1 #negrecip w: 0 2ndspos w: max(x1 + 3, x2 + 4) rnil w: 6 #plus w: 0 square w: x1 + 3 #cons2 w: 0 #square w: 0 pi w: x1 + 11 #rcons w: 0 rcons w: max(x1 + 1, x2) #times w: 0 #mark w: x1 0 w: 3 #posrecip w: 0 from w: x1 + 3 times w: max(x1 + 1, x2 + 2) #s w: 0 mark w: x1 2ndsneg w: max(x1 + 3, x2 + 4) plus w: max(x1 + 2, x2) #2ndspos w: 0 cons2 w: max(x1 + 2, x2) #from w: 0 active w: x1 cons w: max(x1 + 2, x2) #active w: x1 #pi w: 0 #2ndsneg w: 0 posrecip w: x1 + 4 USABLE RULES: { 1..68 } Removed DPs: #24 #31 #34 #35 #44 #51 #70 #73 #77 #78 #82 #83 #89 #95 #108 #113 Number of SCCs: 1, DPs: 15 SCC { #16 #26 #32 #37 #54 #55 #60 #75 #80 #87 #90 #96 #99 #100 #114 } POLO(Sum)... succeeded. negrecip w: 1 #cons w: 0 s w: x1 #negrecip w: 0 2ndspos w: 1 rnil w: 1 #plus w: 0 square w: 1 #cons2 w: 0 #square w: 0 pi w: 1 #rcons w: 0 rcons w: x2 #times w: 0 #mark w: x1 + 1 0 w: 1 #posrecip w: 0 from w: 1 times w: 1 #s w: 0 mark w: x1 2ndsneg w: 1 plus w: x2 #2ndspos w: 0 cons2 w: x2 + 1 #from w: 0 active w: x1 cons w: 1 #active w: x1 + 1 #pi w: 0 #2ndsneg w: 0 posrecip w: 1 USABLE RULES: { 1..68 } Removed DPs: #54 Number of SCCs: 1, DPs: 14 SCC { #16 #26 #32 #37 #55 #60 #75 #80 #87 #90 #96 #99 #100 #114 } POLO(Sum)... POLO(max)... QLPOS... succeeded. negrecip s: [] p: 5 #cons s: [] p: 0 s s: [1] p: 1 #negrecip s: [] p: 0 2ndspos s: [] p: 1 rnil s: [] p: 0 #plus s: [2] p: 0 square s: [1] p: 4 #cons2 s: [1] p: 0 #square s: [] p: 0 pi s: [] p: 4 #rcons s: [2] p: 0 rcons s: 2 #times s: [1,2] p: 0 #mark s: [1] p: 3 0 s: [] p: 3 #posrecip s: [] p: 0 from s: [] p: 1 times s: [1,2] p: 3 #s s: [] p: 0 mark s: 1 2ndsneg s: [] p: 1 plus s: [2,1] p: 2 #2ndspos s: [1] p: 0 cons2 s: [] p: 1 #from s: [] p: 0 active s: 1 cons s: [] p: 1 #active s: [1] p: 3 #pi s: [] p: 0 #2ndsneg s: [2,1] p: 0 posrecip s: [] p: 1 USABLE RULES: { 1..68 } Removed DPs: #26 #60 #90 #99 Number of SCCs: 1, DPs: 7 SCC { #16 #32 #55 #80 #96 #100 #114 } POLO(Sum)... POLO(max)... QLPOS... succeeded. negrecip s: [] p: 2 #cons s: [] p: 0 s s: [1] p: 2 #negrecip s: [] p: 0 2ndspos s: [1] p: 2 rnil s: [] p: 0 #plus s: [2] p: 0 square s: [1] p: 6 #cons2 s: [1] p: 0 #square s: [] p: 0 pi s: [1] p: 2 #rcons s: [2] p: 0 rcons s: [1,2] p: 2 #times s: [1,2] p: 0 #mark s: [1] p: 4 0 s: [] p: 5 #posrecip s: [] p: 0 from s: [] p: 4 times s: [1,2] p: 5 #s s: [] p: 0 mark s: 1 2ndsneg s: [1] p: 2 plus s: [2,1] p: 4 #2ndspos s: [1] p: 0 cons2 s: [] p: 1 #from s: [] p: 0 active s: 1 cons s: [] p: 3 #active s: [1] p: 4 #pi s: [] p: 0 #2ndsneg s: [2,1] p: 0 posrecip s: [] p: 2 USABLE RULES: { 1..68 } Removed DPs: #55 #96 Number of SCCs: 2, DPs: 4 SCC { #80 #100 } POLO(Sum)... succeeded. negrecip w: 1 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: x2 + 1 rnil w: 0 #plus w: 0 square w: 1 #cons2 w: 0 #square w: 0 pi w: 4 #rcons w: 0 rcons w: x1 + 1 #times w: 0 #mark w: x1 + 1 0 w: 0 #posrecip w: 0 from w: 3 times w: 1 #s w: 0 mark w: x1 2ndsneg w: 2 plus w: x2 #2ndspos w: 0 cons2 w: 1 #from w: 0 active w: x1 cons w: 3 #active w: x1 #pi w: 0 #2ndsneg w: 0 posrecip w: 1 USABLE RULES: { 1..68 } Removed DPs: #80 #100 Number of SCCs: 1, DPs: 2 SCC { #16 #32 } POLO(Sum)... succeeded. negrecip w: 1 #cons w: 0 s w: 0 #negrecip w: 0 2ndspos w: x2 + 1 rnil w: 0 #plus w: 0 square w: 1 #cons2 w: 0 #square w: 0 pi w: 4 #rcons w: 0 rcons w: x1 + 1 #times w: 0 #mark w: x1 + 1 0 w: 0 #posrecip w: 0 from w: 3 times w: 1 #s w: 0 mark w: x1 2ndsneg w: x2 + 2 plus w: x2 #2ndspos w: 0 cons2 w: 1 #from w: 0 active w: x1 cons w: 3 #active w: x1 #pi w: 0 #2ndsneg w: 0 posrecip w: 1 USABLE RULES: { 1..68 } Removed DPs: #16 #32 Number of SCCs: 0, DPs: 0