/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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(X) 27: activate(n__length(X)) -> length(X) 28: activate(n__zeros()) -> zeros() 29: activate(n__cons(X1,X2)) -> cons(X1,X2) 30: activate(n__nil()) -> nil() 31: activate(n__take(X1,X2)) -> take(X1,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(X1,X2) #4: #uTake1(tt()) -> #nil() #5: #isNatList(n__cons(N,L)) -> #and(isNat(activate(N)),isNatList(activate(L))) #6: #isNatList(n__cons(N,L)) -> #isNat(activate(N)) #7: #isNatList(n__cons(N,L)) -> #activate(N) #8: #isNatList(n__cons(N,L)) -> #isNatList(activate(L)) #9: #isNatList(n__cons(N,L)) -> #activate(L) #10: #zeros() -> #cons(0(),n__zeros()) #11: #zeros() -> #0() #12: #take(0(),IL) -> #uTake1(isNatIList(IL)) #13: #take(0(),IL) -> #isNatIList(IL) #14: #activate(n__take(X1,X2)) -> #take(X1,X2) #15: #take(s(M),cons(N,IL)) -> #uTake2(and(isNat(M),and(isNat(N),isNatIList(activate(IL)))),M,N,activate(IL)) #16: #take(s(M),cons(N,IL)) -> #and(isNat(M),and(isNat(N),isNatIList(activate(IL)))) #17: #take(s(M),cons(N,IL)) -> #isNat(M) #18: #take(s(M),cons(N,IL)) -> #and(isNat(N),isNatIList(activate(IL))) #19: #take(s(M),cons(N,IL)) -> #isNat(N) #20: #take(s(M),cons(N,IL)) -> #isNatIList(activate(IL)) #21: #take(s(M),cons(N,IL)) -> #activate(IL) #22: #take(s(M),cons(N,IL)) -> #activate(IL) #23: #activate(n__nil()) -> #nil() #24: #activate(n__0()) -> #0() #25: #isNatIList(n__cons(N,IL)) -> #and(isNat(activate(N)),isNatIList(activate(IL))) #26: #isNatIList(n__cons(N,IL)) -> #isNat(activate(N)) #27: #isNatIList(n__cons(N,IL)) -> #activate(N) #28: #isNatIList(n__cons(N,IL)) -> #isNatIList(activate(IL)) #29: #isNatIList(n__cons(N,IL)) -> #activate(IL) #30: #isNatList(n__take(N,IL)) -> #and(isNat(activate(N)),isNatIList(activate(IL))) #31: #isNatList(n__take(N,IL)) -> #isNat(activate(N)) #32: #isNatList(n__take(N,IL)) -> #activate(N) #33: #isNatList(n__take(N,IL)) -> #isNatIList(activate(IL)) #34: #isNatList(n__take(N,IL)) -> #activate(IL) #35: #isNat(n__length(L)) -> #isNatList(activate(L)) #36: #isNat(n__length(L)) -> #activate(L) #37: #activate(n__zeros()) -> #zeros() #38: #activate(n__length(X)) -> #length(X) #39: #uLength(tt(),L) -> #s(length(activate(L))) #40: #uLength(tt(),L) -> #length(activate(L)) #41: #uLength(tt(),L) -> #activate(L) #42: #activate(n__s(X)) -> #s(X) #43: #length(cons(N,L)) -> #uLength(and(isNat(N),isNatList(activate(L))),activate(L)) #44: #length(cons(N,L)) -> #and(isNat(N),isNatList(activate(L))) #45: #length(cons(N,L)) -> #isNat(N) #46: #length(cons(N,L)) -> #isNatList(activate(L)) #47: #length(cons(N,L)) -> #activate(L) #48: #length(cons(N,L)) -> #activate(L) #49: #uTake2(tt(),M,N,IL) -> #cons(activate(N),n__take(activate(M),activate(IL))) #50: #uTake2(tt(),M,N,IL) -> #activate(N) #51: #uTake2(tt(),M,N,IL) -> #activate(M) #52: #uTake2(tt(),M,N,IL) -> #activate(IL) #53: #isNat(n__s(N)) -> #isNat(activate(N)) #54: #isNat(n__s(N)) -> #activate(N) Number of SCCs: 1, DPs: 37 SCC { #1 #2 #6..9 #13..15 #17 #19..22 #26..29 #31..36 #38 #40 #41 #43 #45..48 #50..54 } Sum... succeeded. #uTake2(x1,x2,x3,x4) w: (9726 + x4 + x3 + x2) #0() w: (0) isNatList(x1) w: (592) #cons(x1,x2) w: (0) s(x1) w: (x1) #isNat(x1) w: (9726 + x1) #take(x1,x2) w: (42007 + x2 + x1) activate(x1) w: (x1) take(x1,x2) w: (32283 + x2 + x1) #uTake1(x1) w: (0) and(x1,x2) w: (2 + x1) n__zeros() w: (841) isNatIList(x1) w: (267) #activate(x1) w: (9725 + x1) zeros() w: (841) n__nil() w: (32283) uTake2(x1,x2,x3,x4) w: (32283 + x4 + x3 + x2) n__s(x1) w: (x1) uLength(x1,x2) w: (2450 + x2) 0() w: (0) #zeros() w: (0) n__take(x1,x2) w: (32283 + x2 + x1) #isNatList(x1) w: (9727 + x1) #s(x1) w: (0) n__cons(x1,x2) w: (x2 + x1) nil() w: (32283) #nil() w: (0) n__0() w: (0) n__length(x1) w: (2450 + x1) isNat(x1) w: (591) cons(x1,x2) w: (x2 + x1) #isNatIList(x1) w: (42006 + x1) tt() w: (593) uTake1(x1) w: (32283) length(x1) w: (2450 + x1) #length(x1) w: (9728 + x1) #and(x1,x2) w: (0) #uLength(x1,x2) w: (9728 + x2) USABLE RULES: { 11..32 } Removed DPs: #1 #2 #6 #7 #9 #13..15 #17 #19..22 #26 #27 #29 #31..36 #38 #41 #45..48 #50..52 #54 Number of SCCs: 4, DPs: 5 SCC { #53 } Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... succeeded. #uTake2(x1,x2,x3,x4) w: (0, 0) #0() w: (0, 0) isNatList(x1) w: (56548, 20746 + x1_1) #cons(x1,x2) w: (0, 0) s(x1) w: (126265 + x1_1, 126265 + x1_2) #isNat(x1) w: (13852 + x1_1, x1_2) #take(x1,x2) w: (0, 0) activate(x1) w: (x1_1, 39208 + x1_2) take(x1,x2) w: (174114 + x2_1, 39209 + x2_2 + x1_1 + x1_2) #uTake1(x1) w: (0, 0) and(x1,x2) w: (x2_1, x2_2) n__zeros() w: (8641, 40013) isNatIList(x1) w: (56548, 186219 + x1_1) #activate(x1) w: (0, 0) zeros() w: (8641, 79221) n__nil() w: (174114, 39210) uTake2(x1,x2,x3,x4) w: (174114 + x4_1 + x3_1, 283098 + x4_1 + x4_2 + x2_1 + x2_2) n__s(x1) w: (126265 + x1_1, 87057 + x1_2) uLength(x1,x2) w: (x2_2 + x1_2, 9821 + x2_1 + x2_2 + x1_2) 0() w: (0, 1) #zeros() w: (0, 0) n__take(x1,x2) w: (174114 + x2_1, 1 + x2_2 + x1_1 + x1_2) #isNatList(x1) w: (0, 0) #s(x1) w: (0, 0) n__cons(x1,x2) w: (x2_1 + x1_1, 1 + x2_1 + x2_2) nil() w: (174114, 39210) #nil() w: (0, 0) n__0() w: (0, 0) n__length(x1) w: (29387 + x1_2, x1_1 + x1_2) isNat(x1) w: (26708, 1) cons(x1,x2) w: (x2_1 + x1_1, 30567 + x2_1 + x2_2) #isNatIList(x1) w: (0, 0) tt() w: (56548, 194860) uTake1(x1) w: (174114, 39210) length(x1) w: (29387 + x1_2, 39208 + x1_1 + x1_2) #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: #53 Number of SCCs: 3, DPs: 4 SCC { #28 } 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())) -#28-> #isNatIList(activate(n__zeros())) --->* #isNatIList(n__cons(0(),n__zeros())) Looping with: [ N := 0(); ]