/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO Input TRS: 1: and(tt(),T) -> T 2: isNatIList(IL) -> isNatList(activate(IL)) 3: isNat(n__0()) -> tt() 4: isNat(n__s(N)) -> isNat(activate(N)) 5: isNat(n__length(L)) -> isNatList(activate(L)) 6: isNatIList(n__zeros()) -> tt() 7: isNatIList(n__cons(N,IL)) -> and(isNat(activate(N)),isNatIList(activate(IL))) 8: isNatList(n__nil()) -> tt() 9: isNatList(n__cons(N,L)) -> and(isNat(activate(N)),isNatList(activate(L))) 10: isNatList(n__take(N,IL)) -> and(isNat(activate(N)),isNatIList(activate(IL))) 11: zeros() -> cons(0(),n__zeros()) 12: take(0(),IL) -> uTake1(isNatIList(IL)) 13: uTake1(tt()) -> nil() 14: take(s(M),cons(N,IL)) -> uTake2(and(isNat(M),and(isNat(N),isNatIList(activate(IL)))),M,N,activate(IL)) 15: uTake2(tt(),M,N,IL) -> cons(activate(N),n__take(activate(M),activate(IL))) 16: length(cons(N,L)) -> uLength(and(isNat(N),isNatList(activate(L))),activate(L)) 17: uLength(tt(),L) -> s(length(activate(L))) 18: 0() -> n__0() 19: s(X) -> n__s(X) 20: length(X) -> n__length(X) 21: zeros() -> n__zeros() 22: cons(X1,X2) -> n__cons(X1,X2) 23: nil() -> n__nil() 24: take(X1,X2) -> n__take(X1,X2) 25: activate(n__0()) -> 0() 26: activate(n__s(X)) -> s(activate(X)) 27: activate(n__length(X)) -> length(activate(X)) 28: activate(n__zeros()) -> zeros() 29: activate(n__cons(X1,X2)) -> cons(activate(X1),X2) 30: activate(n__nil()) -> nil() 31: activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) 32: activate(X) -> X Number of strict rules: 32 Direct poly ... failed. Freezing ... failed. Dependency Pairs: #1: #isNatIList(IL) -> #isNatList(activate(IL)) #2: #isNatIList(IL) -> #activate(IL) #3: #activate(n__cons(X1,X2)) -> #cons(activate(X1),X2) #4: #activate(n__cons(X1,X2)) -> #activate(X1) #5: #uTake1(tt()) -> #nil() #6: #isNatList(n__cons(N,L)) -> #and(isNat(activate(N)),isNatList(activate(L))) #7: #isNatList(n__cons(N,L)) -> #isNat(activate(N)) #8: #isNatList(n__cons(N,L)) -> #activate(N) #9: #isNatList(n__cons(N,L)) -> #isNatList(activate(L)) #10: #isNatList(n__cons(N,L)) -> #activate(L) #11: #zeros() -> #cons(0(),n__zeros()) #12: #zeros() -> #0() #13: #take(0(),IL) -> #uTake1(isNatIList(IL)) #14: #take(0(),IL) -> #isNatIList(IL) #15: #activate(n__take(X1,X2)) -> #take(activate(X1),activate(X2)) #16: #activate(n__take(X1,X2)) -> #activate(X1) #17: #activate(n__take(X1,X2)) -> #activate(X2) #18: #take(s(M),cons(N,IL)) -> #uTake2(and(isNat(M),and(isNat(N),isNatIList(activate(IL)))),M,N,activate(IL)) #19: #take(s(M),cons(N,IL)) -> #and(isNat(M),and(isNat(N),isNatIList(activate(IL)))) #20: #take(s(M),cons(N,IL)) -> #isNat(M) #21: #take(s(M),cons(N,IL)) -> #and(isNat(N),isNatIList(activate(IL))) #22: #take(s(M),cons(N,IL)) -> #isNat(N) #23: #take(s(M),cons(N,IL)) -> #isNatIList(activate(IL)) #24: #take(s(M),cons(N,IL)) -> #activate(IL) #25: #take(s(M),cons(N,IL)) -> #activate(IL) #26: #activate(n__nil()) -> #nil() #27: #activate(n__0()) -> #0() #28: #isNatIList(n__cons(N,IL)) -> #and(isNat(activate(N)),isNatIList(activate(IL))) #29: #isNatIList(n__cons(N,IL)) -> #isNat(activate(N)) #30: #isNatIList(n__cons(N,IL)) -> #activate(N) #31: #isNatIList(n__cons(N,IL)) -> #isNatIList(activate(IL)) #32: #isNatIList(n__cons(N,IL)) -> #activate(IL) #33: #isNatList(n__take(N,IL)) -> #and(isNat(activate(N)),isNatIList(activate(IL))) #34: #isNatList(n__take(N,IL)) -> #isNat(activate(N)) #35: #isNatList(n__take(N,IL)) -> #activate(N) #36: #isNatList(n__take(N,IL)) -> #isNatIList(activate(IL)) #37: #isNatList(n__take(N,IL)) -> #activate(IL) #38: #isNat(n__length(L)) -> #isNatList(activate(L)) #39: #isNat(n__length(L)) -> #activate(L) #40: #activate(n__zeros()) -> #zeros() #41: #activate(n__length(X)) -> #length(activate(X)) #42: #activate(n__length(X)) -> #activate(X) #43: #uLength(tt(),L) -> #s(length(activate(L))) #44: #uLength(tt(),L) -> #length(activate(L)) #45: #uLength(tt(),L) -> #activate(L) #46: #activate(n__s(X)) -> #s(activate(X)) #47: #activate(n__s(X)) -> #activate(X) #48: #length(cons(N,L)) -> #uLength(and(isNat(N),isNatList(activate(L))),activate(L)) #49: #length(cons(N,L)) -> #and(isNat(N),isNatList(activate(L))) #50: #length(cons(N,L)) -> #isNat(N) #51: #length(cons(N,L)) -> #isNatList(activate(L)) #52: #length(cons(N,L)) -> #activate(L) #53: #length(cons(N,L)) -> #activate(L) #54: #uTake2(tt(),M,N,IL) -> #cons(activate(N),n__take(activate(M),activate(IL))) #55: #uTake2(tt(),M,N,IL) -> #activate(N) #56: #uTake2(tt(),M,N,IL) -> #activate(M) #57: #uTake2(tt(),M,N,IL) -> #activate(IL) #58: #isNat(n__s(N)) -> #isNat(activate(N)) #59: #isNat(n__s(N)) -> #activate(N) Number of SCCs: 1, DPs: 42 SCC { #1 #2 #4 #7..10 #14..18 #20 #22..25 #29..32 #34..39 #41 #42 #44 #45 #47 #48 #50..53 #55..59 } Sum... succeeded. #uTake2(x1,x2,x3,x4) w: (878 + x4 + x3 + x2) #0() w: (0) isNatList(x1) w: (5) #cons(x1,x2) w: (0) s(x1) w: (x1) #isNat(x1) w: (2 + x1) #take(x1,x2) w: (2245 + x2 + x1) activate(x1) w: (x1) take(x1,x2) w: (2245 + x2 + x1) #uTake1(x1) w: (0) and(x1,x2) w: (x2) n__zeros() w: (9726) isNatIList(x1) w: (5) #activate(x1) w: (1 + x1) zeros() w: (9726) n__nil() w: (1) uTake2(x1,x2,x3,x4) w: (2240 + x4 + x3 + x2 + x1) n__s(x1) w: (x1) uLength(x1,x2) w: (2244 + x2) 0() w: (0) #zeros() w: (0) n__take(x1,x2) w: (2245 + x2 + x1) #isNatList(x1) w: (2243 + x1) #s(x1) w: (0) n__cons(x1,x2) w: (x2 + x1) nil() w: (1) #nil() w: (0) n__0() w: (0) n__length(x1) w: (2244 + x1) isNat(x1) w: (4) cons(x1,x2) w: (x2 + x1) #isNatIList(x1) w: (2244 + x1) tt() w: (5) uTake1(x1) w: (x1) length(x1) w: (2244 + x1) #length(x1) w: (2244 + x1) #and(x1,x2) w: (0) #uLength(x1,x2) w: (2244 + x2) USABLE RULES: { 1 2 6..32 } Removed DPs: #1 #2 #7 #8 #10 #14..18 #20 #22..25 #29 #30 #32 #34..39 #41 #42 #45 #50..53 #55..57 #59 Number of SCCs: 5, DPs: 7 SCC { #58 } Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... succeeded. #uTake2(x1,x2,x3,x4) w: (0, 0) #0() w: (0, 0) isNatList(x1) w: (75667 + x1_1 + x1_2, 3 + x1_2) #cons(x1,x2) w: (0, 0) s(x1) w: (48047 + x1_2, 27866 + x1_1) #isNat(x1) w: (x1_1 + x1_2, 0) #take(x1,x2) w: (0, 0) activate(x1) w: (x1_1, x1_2) take(x1,x2) w: (65881 + x2_1 + x1_1 + x1_2, 75913 + x2_2) #uTake1(x1) w: (0, 0) and(x1,x2) w: (x2_1, x2_2) n__zeros() w: (5639, 0) isNatIList(x1) w: (75667 + x1_1 + x1_2, 75916 + x1_2) #activate(x1) w: (0, 0) zeros() w: (5639, 0) n__nil() w: (5334, 75913) uTake2(x1,x2,x3,x4) w: (141794 + x4_1 + x4_2 + x2_1 + x2_2, 75913 + x4_2) n__s(x1) w: (48047 + x1_2, 27866 + x1_1) uLength(x1,x2) w: (48050 + x2_1, x2_1 + x1_2) 0() w: (3917, 20623) #zeros() w: (0, 0) n__take(x1,x2) w: (65881 + x2_1 + x1_1 + x1_2, 75913 + x2_2) #isNatList(x1) w: (0, 0) #s(x1) w: (0, 0) n__cons(x1,x2) w: (x2_1 + x2_2, x2_2) nil() w: (5334, 75913) #nil() w: (0, 0) n__0() w: (3917, 20623) n__length(x1) w: (48050 + x1_1, 3 + x1_1) isNat(x1) w: (27613 + x1_1 + x1_2, 12646 + x1_1 + x1_2) cons(x1,x2) w: (x2_1 + x2_2, x2_2) #isNatIList(x1) w: (0, 0) tt() w: (52154, 75916) uTake1(x1) w: (5336, 75913) length(x1) w: (48050 + x1_1, 3 + x1_1) #length(x1) w: (0, 0) #and(x1,x2) w: (0, 0) #uLength(x1,x2) w: (0, 0) USABLE RULES: { 1 2 6..32 } Removed DPs: #58 Number of SCCs: 4, DPs: 6 SCC { #31 } Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... sum_sum_int,sum_neg... heuristic_int,sum_neg... failed. Finding a loop... found. #isNatIList(n__cons(N,n__zeros())) -#31-> #isNatIList(activate(n__zeros())) --->* #isNatIList(n__cons(0(),n__zeros())) Looping with: [ N := 0(); ]