/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE 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: active(s(X)) -> s(active(X)) 15: active(posrecip(X)) -> posrecip(active(X)) 16: active(negrecip(X)) -> negrecip(active(X)) 17: active(cons(X1,X2)) -> cons(active(X1),X2) 18: active(cons2(X1,X2)) -> cons2(X1,active(X2)) 19: active(rcons(X1,X2)) -> rcons(active(X1),X2) 20: active(rcons(X1,X2)) -> rcons(X1,active(X2)) 21: active(from(X)) -> from(active(X)) 22: active(2ndspos(X1,X2)) -> 2ndspos(active(X1),X2) 23: active(2ndspos(X1,X2)) -> 2ndspos(X1,active(X2)) 24: active(2ndsneg(X1,X2)) -> 2ndsneg(active(X1),X2) 25: active(2ndsneg(X1,X2)) -> 2ndsneg(X1,active(X2)) 26: active(pi(X)) -> pi(active(X)) 27: active(plus(X1,X2)) -> plus(active(X1),X2) 28: active(plus(X1,X2)) -> plus(X1,active(X2)) 29: active(times(X1,X2)) -> times(active(X1),X2) 30: active(times(X1,X2)) -> times(X1,active(X2)) 31: active(square(X)) -> square(active(X)) 32: s(mark(X)) -> mark(s(X)) 33: posrecip(mark(X)) -> mark(posrecip(X)) 34: negrecip(mark(X)) -> mark(negrecip(X)) 35: cons(mark(X1),X2) -> mark(cons(X1,X2)) 36: cons2(X1,mark(X2)) -> mark(cons2(X1,X2)) 37: rcons(mark(X1),X2) -> mark(rcons(X1,X2)) 38: rcons(X1,mark(X2)) -> mark(rcons(X1,X2)) 39: from(mark(X)) -> mark(from(X)) 40: 2ndspos(mark(X1),X2) -> mark(2ndspos(X1,X2)) 41: 2ndspos(X1,mark(X2)) -> mark(2ndspos(X1,X2)) 42: 2ndsneg(mark(X1),X2) -> mark(2ndsneg(X1,X2)) 43: 2ndsneg(X1,mark(X2)) -> mark(2ndsneg(X1,X2)) 44: pi(mark(X)) -> mark(pi(X)) 45: plus(mark(X1),X2) -> mark(plus(X1,X2)) 46: plus(X1,mark(X2)) -> mark(plus(X1,X2)) 47: times(mark(X1),X2) -> mark(times(X1,X2)) 48: times(X1,mark(X2)) -> mark(times(X1,X2)) 49: square(mark(X)) -> mark(square(X)) 50: proper(0()) -> ok(0()) 51: proper(s(X)) -> s(proper(X)) 52: proper(posrecip(X)) -> posrecip(proper(X)) 53: proper(negrecip(X)) -> negrecip(proper(X)) 54: proper(nil()) -> ok(nil()) 55: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 56: proper(cons2(X1,X2)) -> cons2(proper(X1),proper(X2)) 57: proper(rnil()) -> ok(rnil()) 58: proper(rcons(X1,X2)) -> rcons(proper(X1),proper(X2)) 59: proper(from(X)) -> from(proper(X)) 60: proper(2ndspos(X1,X2)) -> 2ndspos(proper(X1),proper(X2)) 61: proper(2ndsneg(X1,X2)) -> 2ndsneg(proper(X1),proper(X2)) 62: proper(pi(X)) -> pi(proper(X)) 63: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) 64: proper(times(X1,X2)) -> times(proper(X1),proper(X2)) 65: proper(square(X)) -> square(proper(X)) 66: s(ok(X)) -> ok(s(X)) 67: posrecip(ok(X)) -> ok(posrecip(X)) 68: negrecip(ok(X)) -> ok(negrecip(X)) 69: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 70: cons2(ok(X1),ok(X2)) -> ok(cons2(X1,X2)) 71: rcons(ok(X1),ok(X2)) -> ok(rcons(X1,X2)) 72: from(ok(X)) -> ok(from(X)) 73: 2ndspos(ok(X1),ok(X2)) -> ok(2ndspos(X1,X2)) 74: 2ndsneg(ok(X1),ok(X2)) -> ok(2ndsneg(X1,X2)) 75: pi(ok(X)) -> ok(pi(X)) 76: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) 77: times(ok(X1),ok(X2)) -> ok(times(X1,X2)) 78: square(ok(X)) -> ok(square(X)) 79: top(mark(X)) -> top(proper(X)) 80: top(ok(X)) -> top(active(X)) Number of strict rules: 80 Direct poly ... failed. Freezing ... failed. Dependency Pairs: #1: #2ndsneg(X1,mark(X2)) -> #2ndsneg(X1,X2) #2: #active(times(X1,X2)) -> #times(active(X1),X2) #3: #active(times(X1,X2)) -> #active(X1) #4: #cons(mark(X1),X2) -> #cons(X1,X2) #5: #s(ok(X)) -> #s(X) #6: #plus(X1,mark(X2)) -> #plus(X1,X2) #7: #2ndsneg(mark(X1),X2) -> #2ndsneg(X1,X2) #8: #2ndspos(X1,mark(X2)) -> #2ndspos(X1,X2) #9: #rcons(mark(X1),X2) -> #rcons(X1,X2) #10: #2ndspos(ok(X1),ok(X2)) -> #2ndspos(X1,X2) #11: #times(mark(X1),X2) -> #times(X1,X2) #12: #proper(negrecip(X)) -> #negrecip(proper(X)) #13: #proper(negrecip(X)) -> #proper(X) #14: #rcons(ok(X1),ok(X2)) -> #rcons(X1,X2) #15: #times(X1,mark(X2)) -> #times(X1,X2) #16: #pi(ok(X)) -> #pi(X) #17: #2ndsneg(ok(X1),ok(X2)) -> #2ndsneg(X1,X2) #18: #proper(rcons(X1,X2)) -> #rcons(proper(X1),proper(X2)) #19: #proper(rcons(X1,X2)) -> #proper(X1) #20: #proper(rcons(X1,X2)) -> #proper(X2) #21: #proper(2ndsneg(X1,X2)) -> #2ndsneg(proper(X1),proper(X2)) #22: #proper(2ndsneg(X1,X2)) -> #proper(X1) #23: #proper(2ndsneg(X1,X2)) -> #proper(X2) #24: #rcons(X1,mark(X2)) -> #rcons(X1,X2) #25: #active(2ndsneg(s(N),cons(X,Z))) -> #2ndsneg(s(N),cons2(X,Z)) #26: #active(2ndsneg(s(N),cons(X,Z))) -> #cons2(X,Z) #27: #proper(from(X)) -> #from(proper(X)) #28: #proper(from(X)) -> #proper(X) #29: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2)) #30: #proper(cons(X1,X2)) -> #proper(X1) #31: #proper(cons(X1,X2)) -> #proper(X2) #32: #posrecip(ok(X)) -> #posrecip(X) #33: #2ndspos(mark(X1),X2) -> #2ndspos(X1,X2) #34: #proper(s(X)) -> #s(proper(X)) #35: #proper(s(X)) -> #proper(X) #36: #active(square(X)) -> #times(X,X) #37: #plus(ok(X1),ok(X2)) -> #plus(X1,X2) #38: #active(2ndsneg(X1,X2)) -> #2ndsneg(active(X1),X2) #39: #active(2ndsneg(X1,X2)) -> #active(X1) #40: #cons2(ok(X1),ok(X2)) -> #cons2(X1,X2) #41: #active(2ndspos(X1,X2)) -> #2ndspos(X1,active(X2)) #42: #active(2ndspos(X1,X2)) -> #active(X2) #43: #square(ok(X)) -> #square(X) #44: #plus(mark(X1),X2) -> #plus(X1,X2) #45: #cons(ok(X1),ok(X2)) -> #cons(X1,X2) #46: #active(times(s(X),Y)) -> #plus(Y,times(X,Y)) #47: #active(times(s(X),Y)) -> #times(X,Y) #48: #active(square(X)) -> #square(active(X)) #49: #active(square(X)) -> #active(X) #50: #top(mark(X)) -> #top(proper(X)) #51: #top(mark(X)) -> #proper(X) #52: #proper(cons2(X1,X2)) -> #cons2(proper(X1),proper(X2)) #53: #proper(cons2(X1,X2)) -> #proper(X1) #54: #proper(cons2(X1,X2)) -> #proper(X2) #55: #active(s(X)) -> #s(active(X)) #56: #active(s(X)) -> #active(X) #57: #proper(pi(X)) -> #pi(proper(X)) #58: #proper(pi(X)) -> #proper(X) #59: #active(times(X1,X2)) -> #times(X1,active(X2)) #60: #active(times(X1,X2)) -> #active(X2) #61: #proper(posrecip(X)) -> #posrecip(proper(X)) #62: #proper(posrecip(X)) -> #proper(X) #63: #square(mark(X)) -> #square(X) #64: #active(2ndsneg(X1,X2)) -> #2ndsneg(X1,active(X2)) #65: #active(2ndsneg(X1,X2)) -> #active(X2) #66: #active(rcons(X1,X2)) -> #rcons(X1,active(X2)) #67: #active(rcons(X1,X2)) -> #active(X2) #68: #active(2ndsneg(s(N),cons2(X,cons(Y,Z)))) -> #rcons(negrecip(Y),2ndspos(N,Z)) #69: #active(2ndsneg(s(N),cons2(X,cons(Y,Z)))) -> #negrecip(Y) #70: #active(2ndsneg(s(N),cons2(X,cons(Y,Z)))) -> #2ndspos(N,Z) #71: #from(mark(X)) -> #from(X) #72: #active(plus(s(X),Y)) -> #s(plus(X,Y)) #73: #active(plus(s(X),Y)) -> #plus(X,Y) #74: #proper(times(X1,X2)) -> #times(proper(X1),proper(X2)) #75: #proper(times(X1,X2)) -> #proper(X1) #76: #proper(times(X1,X2)) -> #proper(X2) #77: #posrecip(mark(X)) -> #posrecip(X) #78: #from(ok(X)) -> #from(X) #79: #pi(mark(X)) -> #pi(X) #80: #proper(square(X)) -> #square(proper(X)) #81: #proper(square(X)) -> #proper(X) #82: #active(plus(X1,X2)) -> #plus(X1,active(X2)) #83: #active(plus(X1,X2)) -> #active(X2) #84: #active(2ndspos(X1,X2)) -> #2ndspos(active(X1),X2) #85: #active(2ndspos(X1,X2)) -> #active(X1) #86: #negrecip(mark(X)) -> #negrecip(X) #87: #active(plus(X1,X2)) -> #plus(active(X1),X2) #88: #active(plus(X1,X2)) -> #active(X1) #89: #proper(2ndspos(X1,X2)) -> #2ndspos(proper(X1),proper(X2)) #90: #proper(2ndspos(X1,X2)) -> #proper(X1) #91: #proper(2ndspos(X1,X2)) -> #proper(X2) #92: #active(cons(X1,X2)) -> #cons(active(X1),X2) #93: #active(cons(X1,X2)) -> #active(X1) #94: #s(mark(X)) -> #s(X) #95: #active(rcons(X1,X2)) -> #rcons(active(X1),X2) #96: #active(rcons(X1,X2)) -> #active(X1) #97: #proper(plus(X1,X2)) -> #plus(proper(X1),proper(X2)) #98: #proper(plus(X1,X2)) -> #proper(X1) #99: #proper(plus(X1,X2)) -> #proper(X2) #100: #active(pi(X)) -> #pi(active(X)) #101: #active(pi(X)) -> #active(X) #102: #negrecip(ok(X)) -> #negrecip(X) #103: #cons2(X1,mark(X2)) -> #cons2(X1,X2) #104: #active(from(X)) -> #from(active(X)) #105: #active(from(X)) -> #active(X) #106: #active(negrecip(X)) -> #negrecip(active(X)) #107: #active(negrecip(X)) -> #active(X) #108: #active(2ndspos(s(N),cons(X,Z))) -> #2ndspos(s(N),cons2(X,Z)) #109: #active(2ndspos(s(N),cons(X,Z))) -> #cons2(X,Z) #110: #times(ok(X1),ok(X2)) -> #times(X1,X2) #111: #active(from(X)) -> #cons(X,from(s(X))) #112: #active(from(X)) -> #from(s(X)) #113: #active(from(X)) -> #s(X) #114: #active(pi(X)) -> #2ndspos(X,from(0())) #115: #active(pi(X)) -> #from(0()) #116: #active(posrecip(X)) -> #posrecip(active(X)) #117: #active(posrecip(X)) -> #active(X) #118: #active(2ndspos(s(N),cons2(X,cons(Y,Z)))) -> #rcons(posrecip(Y),2ndsneg(N,Z)) #119: #active(2ndspos(s(N),cons2(X,cons(Y,Z)))) -> #posrecip(Y) #120: #active(2ndspos(s(N),cons2(X,cons(Y,Z)))) -> #2ndsneg(N,Z) #121: #top(ok(X)) -> #top(active(X)) #122: #top(ok(X)) -> #active(X) #123: #active(cons2(X1,X2)) -> #cons2(X1,active(X2)) #124: #active(cons2(X1,X2)) -> #active(X2) Number of SCCs: 16, DPs: 71 SCC { #86 #102 } Sum... succeeded. negrecip(x1) w: (0) #cons(x1,x2) w: (0) s(x1) w: (0) #negrecip(x1) w: (x1) 2ndspos(x1,x2) w: (0) top(x1) w: (0) rnil() w: (0) #plus(x1,x2) w: (0) square(x1) w: (0) #top(x1) w: (0) #cons2(x1,x2) w: (0) #square(x1) w: (0) pi(x1) w: (0) #rcons(x1,x2) w: (0) rcons(x1,x2) w: (0) proper(x1) w: (0) ok(x1) w: (1 + x1) #times(x1,x2) w: (0) 0() w: (0) #posrecip(x1) w: (0) from(x1) w: (0) times(x1,x2) w: (0) #s(x1) w: (0) nil() w: (0) mark(x1) w: (1 + x1) 2ndsneg(x1,x2) w: (0) #proper(x1) w: (0) plus(x1,x2) w: (0) #2ndspos(x1,x2) w: (0) cons2(x1,x2) w: (0) #from(x1) w: (0) active(x1) w: (0) cons(x1,x2) w: (0) #active(x1) w: (0) #pi(x1) w: (0) #2ndsneg(x1,x2) w: (0) posrecip(x1) w: (0) USABLE RULES: { } Removed DPs: #86 #102 Number of SCCs: 15, DPs: 69 SCC { #71 #78 } Sum... succeeded. negrecip(x1) w: (0) #cons(x1,x2) w: (0) s(x1) w: (0) #negrecip(x1) w: (0) 2ndspos(x1,x2) w: (0) top(x1) w: (0) rnil() w: (0) #plus(x1,x2) w: (0) square(x1) w: (0) #top(x1) w: (0) #cons2(x1,x2) w: (0) #square(x1) w: (0) pi(x1) w: (0) #rcons(x1,x2) w: (0) rcons(x1,x2) w: (0) proper(x1) w: (0) ok(x1) w: (1 + x1) #times(x1,x2) w: (0) 0() w: (0) #posrecip(x1) w: (0) from(x1) w: (0) times(x1,x2) w: (0) #s(x1) w: (0) nil() w: (0) mark(x1) w: (1 + x1) 2ndsneg(x1,x2) w: (0) #proper(x1) w: (0) plus(x1,x2) w: (0) #2ndspos(x1,x2) w: (0) cons2(x1,x2) w: (0) #from(x1) w: (x1) active(x1) w: (0) cons(x1,x2) w: (0) #active(x1) w: (0) #pi(x1) w: (0) #2ndsneg(x1,x2) w: (0) posrecip(x1) w: (0) USABLE RULES: { } Removed DPs: #71 #78 Number of SCCs: 14, DPs: 67 SCC { #5 #94 } Sum... succeeded. negrecip(x1) w: (0) #cons(x1,x2) w: (0) s(x1) w: (0) #negrecip(x1) w: (0) 2ndspos(x1,x2) w: (0) top(x1) w: (0) rnil() w: (0) #plus(x1,x2) w: (0) square(x1) w: (0) #top(x1) w: (0) #cons2(x1,x2) w: (0) #square(x1) w: (0) pi(x1) w: (0) #rcons(x1,x2) w: (0) rcons(x1,x2) w: (0) proper(x1) w: (0) ok(x1) w: (1 + x1) #times(x1,x2) w: (0) 0() w: (0) #posrecip(x1) w: (0) from(x1) w: (0) times(x1,x2) w: (0) #s(x1) w: (x1) nil() w: (0) mark(x1) w: (1 + x1) 2ndsneg(x1,x2) w: (0) #proper(x1) w: (0) plus(x1,x2) w: (0) #2ndspos(x1,x2) w: (0) cons2(x1,x2) w: (0) #from(x1) w: (0) active(x1) w: (0) cons(x1,x2) w: (0) #active(x1) w: (0) #pi(x1) w: (0) #2ndsneg(x1,x2) w: (0) posrecip(x1) w: (0) USABLE RULES: { } Removed DPs: #5 #94 Number of SCCs: 13, DPs: 65 SCC { #16 #79 } Sum... succeeded. negrecip(x1) w: (0) #cons(x1,x2) w: (0) s(x1) w: (0) #negrecip(x1) w: (0) 2ndspos(x1,x2) w: (0) top(x1) w: (0) rnil() w: (0) #plus(x1,x2) w: (0) square(x1) w: (0) #top(x1) w: (0) #cons2(x1,x2) w: (0) #square(x1) w: (0) pi(x1) w: (0) #rcons(x1,x2) w: (0) rcons(x1,x2) w: (0) proper(x1) w: (0) ok(x1) w: (1 + x1) #times(x1,x2) w: (0) 0() w: (0) #posrecip(x1) w: (0) from(x1) w: (0) times(x1,x2) w: (0) #s(x1) w: (0) nil() w: (0) mark(x1) w: (1 + x1) 2ndsneg(x1,x2) w: (0) #proper(x1) w: (0) plus(x1,x2) w: (0) #2ndspos(x1,x2) w: (0) cons2(x1,x2) w: (0) #from(x1) w: (0) active(x1) w: (0) cons(x1,x2) w: (0) #active(x1) w: (0) #pi(x1) w: (x1) #2ndsneg(x1,x2) w: (0) posrecip(x1) w: (0) USABLE RULES: { } Removed DPs: #16 #79 Number of SCCs: 12, DPs: 63 SCC { #32 #77 } Sum... succeeded. negrecip(x1) w: (0) #cons(x1,x2) w: (0) s(x1) w: (0) #negrecip(x1) w: (0) 2ndspos(x1,x2) w: (0) top(x1) w: (0) rnil() w: (0) #plus(x1,x2) w: (0) square(x1) w: (0) #top(x1) w: (0) #cons2(x1,x2) w: (0) #square(x1) w: (0) pi(x1) w: (0) #rcons(x1,x2) w: (0) rcons(x1,x2) w: (0) proper(x1) w: (0) ok(x1) w: (1 + x1) #times(x1,x2) w: (0) 0() w: (0) #posrecip(x1) w: (x1) from(x1) w: (0) times(x1,x2) w: (0) #s(x1) w: (0) nil() w: (0) mark(x1) w: (1 + x1) 2ndsneg(x1,x2) w: (0) #proper(x1) w: (0) plus(x1,x2) w: (0) #2ndspos(x1,x2) w: (0) cons2(x1,x2) w: (0) #from(x1) w: (0) active(x1) w: (0) cons(x1,x2) w: (0) #active(x1) w: (0) #pi(x1) w: (0) #2ndsneg(x1,x2) w: (0) posrecip(x1) w: (0) USABLE RULES: { } Removed DPs: #32 #77 Number of SCCs: 11, DPs: 61 SCC { #43 #63 } Sum... succeeded. negrecip(x1) w: (0) #cons(x1,x2) w: (0) s(x1) w: (0) #negrecip(x1) w: (0) 2ndspos(x1,x2) w: (0) top(x1) w: (0) rnil() w: (0) #plus(x1,x2) w: (0) square(x1) w: (0) #top(x1) w: (0) #cons2(x1,x2) w: (0) #square(x1) w: (x1) pi(x1) w: (0) #rcons(x1,x2) w: (0) rcons(x1,x2) w: (0) proper(x1) w: (0) ok(x1) w: (1 + x1) #times(x1,x2) w: (0) 0() w: (0) #posrecip(x1) w: (0) from(x1) w: (0) times(x1,x2) w: (0) #s(x1) w: (0) nil() w: (0) mark(x1) w: (1 + x1) 2ndsneg(x1,x2) w: (0) #proper(x1) w: (0) plus(x1,x2) w: (0) #2ndspos(x1,x2) w: (0) cons2(x1,x2) w: (0) #from(x1) w: (0) active(x1) w: (0) cons(x1,x2) w: (0) #active(x1) w: (0) #pi(x1) w: (0) #2ndsneg(x1,x2) w: (0) posrecip(x1) w: (0) USABLE RULES: { } Removed DPs: #43 #63 Number of SCCs: 10, DPs: 59 SCC { #50 #121 } Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... sum_sum_int,sum_neg... heuristic_int,sum_neg... failed. Finding a loop... failed.