/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: a__from(X) -> cons(mark(X),from(s(X))) 2: a__sel(0(),cons(X,XS)) -> mark(X) 3: a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS)) 4: a__minus(X,0()) -> 0() 5: a__minus(s(X),s(Y)) -> a__minus(mark(X),mark(Y)) 6: a__quot(0(),s(Y)) -> 0() 7: a__quot(s(X),s(Y)) -> s(a__quot(a__minus(mark(X),mark(Y)),s(mark(Y)))) 8: a__zWquot(XS,nil()) -> nil() 9: a__zWquot(nil(),XS) -> nil() 10: a__zWquot(cons(X,XS),cons(Y,YS)) -> cons(a__quot(mark(X),mark(Y)),zWquot(XS,YS)) 11: mark(from(X)) -> a__from(mark(X)) 12: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) 13: mark(minus(X1,X2)) -> a__minus(mark(X1),mark(X2)) 14: mark(quot(X1,X2)) -> a__quot(mark(X1),mark(X2)) 15: mark(zWquot(X1,X2)) -> a__zWquot(mark(X1),mark(X2)) 16: mark(cons(X1,X2)) -> cons(mark(X1),X2) 17: mark(s(X)) -> s(mark(X)) 18: mark(0()) -> 0() 19: mark(nil()) -> nil() 20: a__from(X) -> from(X) 21: a__sel(X1,X2) -> sel(X1,X2) 22: a__minus(X1,X2) -> minus(X1,X2) 23: a__quot(X1,X2) -> quot(X1,X2) 24: a__zWquot(X1,X2) -> zWquot(X1,X2) Number of strict rules: 24 Direct poly ... failed. Freezing ... failed. Dependency Pairs: #1: #a__sel(0(),cons(X,XS)) -> #mark(X) #2: #mark(minus(X1,X2)) -> #a__minus(mark(X1),mark(X2)) #3: #mark(minus(X1,X2)) -> #mark(X1) #4: #mark(minus(X1,X2)) -> #mark(X2) #5: #mark(from(X)) -> #a__from(mark(X)) #6: #mark(from(X)) -> #mark(X) #7: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2)) #8: #mark(sel(X1,X2)) -> #mark(X1) #9: #mark(sel(X1,X2)) -> #mark(X2) #10: #mark(quot(X1,X2)) -> #a__quot(mark(X1),mark(X2)) #11: #mark(quot(X1,X2)) -> #mark(X1) #12: #mark(quot(X1,X2)) -> #mark(X2) #13: #a__quot(s(X),s(Y)) -> #a__quot(a__minus(mark(X),mark(Y)),s(mark(Y))) #14: #a__quot(s(X),s(Y)) -> #a__minus(mark(X),mark(Y)) #15: #a__quot(s(X),s(Y)) -> #mark(X) #16: #a__quot(s(X),s(Y)) -> #mark(Y) #17: #a__quot(s(X),s(Y)) -> #mark(Y) #18: #a__zWquot(cons(X,XS),cons(Y,YS)) -> #a__quot(mark(X),mark(Y)) #19: #a__zWquot(cons(X,XS),cons(Y,YS)) -> #mark(X) #20: #a__zWquot(cons(X,XS),cons(Y,YS)) -> #mark(Y) #21: #a__minus(s(X),s(Y)) -> #a__minus(mark(X),mark(Y)) #22: #a__minus(s(X),s(Y)) -> #mark(X) #23: #a__minus(s(X),s(Y)) -> #mark(Y) #24: #mark(s(X)) -> #mark(X) #25: #mark(cons(X1,X2)) -> #mark(X1) #26: #a__sel(s(N),cons(X,XS)) -> #a__sel(mark(N),mark(XS)) #27: #a__sel(s(N),cons(X,XS)) -> #mark(N) #28: #a__sel(s(N),cons(X,XS)) -> #mark(XS) #29: #a__from(X) -> #mark(X) #30: #mark(zWquot(X1,X2)) -> #a__zWquot(mark(X1),mark(X2)) #31: #mark(zWquot(X1,X2)) -> #mark(X1) #32: #mark(zWquot(X1,X2)) -> #mark(X2) Number of SCCs: 1, DPs: 31 SCC { #1..12 #14..32 } Sum... Max... succeeded. a__minus(x1,x2) w: (max{x2, x1}) s(x1) w: (x1) #a__zWquot(x1,x2) w: (max{42200 + x2, 42199 + x1}) #a__from(x1) w: (59107 + x1) #a__quot(x1,x2) w: (max{42199 + x2, 42199 + x1}) minus(x1,x2) w: (max{x2, x1}) a__from(x1) w: (16909 + x1) a__zWquot(x1,x2) w: (max{21239 + x2, x1}) zWquot(x1,x2) w: (max{21239 + x2, x1}) a__quot(x1,x2) w: (max{x2, x1}) #mark(x1) w: (42199 + x1) 0() w: (0) quot(x1,x2) w: (max{x2, x1}) from(x1) w: (16909 + x1) sel(x1,x2) w: (max{x2, x1}) #a__minus(x1,x2) w: (max{42199 + x2, 42199 + x1}) nil() w: (0) #a__sel(x1,x2) w: (max{42199 + x2, 42199 + x1}) mark(x1) w: (x1) a__sel(x1,x2) w: (max{x2, x1}) cons(x1,x2) w: (max{x2, x1}) USABLE RULES: { 1..24 } Removed DPs: #5 #6 #20 #29 #32 Number of SCCs: 1, DPs: 26 SCC { #1..4 #7..12 #14..19 #21..28 #30 #31 } Sum... Max... succeeded. a__minus(x1,x2) w: (max{x2, x1}) s(x1) w: (x1) #a__zWquot(x1,x2) w: (max{66696 + x2, 48808 + x1}) #a__from(x1) w: (59107 + x1) #a__quot(x1,x2) w: (max{48808 + x2, 48808 + x1}) minus(x1,x2) w: (max{x2, x1}) a__from(x1) w: (48506 + x1) a__zWquot(x1,x2) w: (max{17889 + x2, x1}) zWquot(x1,x2) w: (max{17889 + x2, x1}) a__quot(x1,x2) w: (max{x2, x1}) #mark(x1) w: (48808 + x1) 0() w: (0) quot(x1,x2) w: (max{x2, x1}) from(x1) w: (48506 + x1) sel(x1,x2) w: (max{6881 + x2, 6881 + x1}) #a__minus(x1,x2) w: (max{48808 + x2, 48808 + x1}) nil() w: (0) #a__sel(x1,x2) w: (max{55688 + x2, 55687 + x1}) mark(x1) w: (x1) a__sel(x1,x2) w: (max{6881 + x2, 6881 + x1}) cons(x1,x2) w: (max{x2, x1}) USABLE RULES: { 1..24 } Removed DPs: #1 #7..9 #27 #28 Number of SCCs: 2, DPs: 20 SCC { #26 } Sum... Max... QLPOpS... NegMaxSum... succeeded. a__minus(x1,x2) w: (0) s(x1) w: (max{0, 2 + x1}) #a__zWquot(x1,x2) w: (0) #a__from(x1) w: (0) #a__quot(x1,x2) w: (0) minus(x1,x2) w: (0) a__from(x1) w: (max{0, 3 + x1}) a__zWquot(x1,x2) w: (max{0, 2 + x1}) zWquot(x1,x2) w: (max{0, 2 + x1}) a__quot(x1,x2) w: (max{0, 1 + x1}) #mark(x1) w: (0) 0() w: (0) quot(x1,x2) w: (max{0, 1 + x1}) from(x1) w: (max{0, 3 + x1}) sel(x1,x2) w: (max{0, -1 + x2 + x1}) #a__minus(x1,x2) w: (0) nil() w: (1) #a__sel(x1,x2) w: (max{0, 1324 + x1}) mark(x1) w: (max{0, x1}) a__sel(x1,x2) w: (max{0, -1 + x2 + x1}) cons(x1,x2) w: (max{0, -2 + x2, 3 + x1}) USABLE RULES: { 1..24 } Removed DPs: #26 Number of SCCs: 1, DPs: 19 SCC { #2..4 #10..12 #14..19 #21..25 #30 #31 } Sum... Max... succeeded. a__minus(x1,x2) w: (max{2 + x2, x1}) s(x1) w: (x1) #a__zWquot(x1,x2) w: (max{26340 + x2, 68255 + x1}) #a__from(x1) w: (59107) #a__quot(x1,x2) w: (max{41265 + x2, 41265 + x1}) minus(x1,x2) w: (max{2 + x2, x1}) a__from(x1) w: (14926 + x1) a__zWquot(x1,x2) w: (max{26991 + x2, 26993 + x1}) zWquot(x1,x2) w: (max{26991 + x2, 26993 + x1}) a__quot(x1,x2) w: (max{12068 + x2, 12065 + x1}) #mark(x1) w: (41263 + x1) 0() w: (0) quot(x1,x2) w: (max{12068 + x2, 12065 + x1}) from(x1) w: (14926 + x1) sel(x1,x2) w: (max{1 + x2, 2 + x1}) #a__minus(x1,x2) w: (max{41264 + x2, 41263 + x1}) nil() w: (26994) #a__sel(x1,x2) w: (0) mark(x1) w: (x1) a__sel(x1,x2) w: (max{1 + x2, 2 + x1}) cons(x1,x2) w: (max{x2, 14926 + x1}) USABLE RULES: { 1..24 } Removed DPs: #4 #10..12 #14..19 #23 #25 #30 #31 Number of SCCs: 1, DPs: 5 SCC { #2 #3 #21 #22 #24 } Sum... Max... succeeded. a__minus(x1,x2) w: (max{23977 + x2, 23976 + x1}) s(x1) w: (x1) #a__zWquot(x1,x2) w: (0) #a__from(x1) w: (59107) #a__quot(x1,x2) w: (0) minus(x1,x2) w: (max{23977 + x2, 23976 + x1}) a__from(x1) w: (8822 + x1) a__zWquot(x1,x2) w: (max{0, 1 + x1}) zWquot(x1,x2) w: (max{0, 1 + x1}) a__quot(x1,x2) w: (0) #mark(x1) w: (1 + x1) 0() w: (0) quot(x1,x2) w: (0) from(x1) w: (8822 + x1) sel(x1,x2) w: (max{x2, 0}) #a__minus(x1,x2) w: (max{0, 23976 + x1}) nil() w: (1) #a__sel(x1,x2) w: (0) mark(x1) w: (x1) a__sel(x1,x2) w: (max{x2, 0}) cons(x1,x2) w: (max{x2, x1}) USABLE RULES: { 1..24 } Removed DPs: #2 #3 #22 Number of SCCs: 2, DPs: 2 SCC { #24 } Sum... succeeded. a__minus(x1,x2) w: (1 + x2) s(x1) w: (1 + x1) #a__zWquot(x1,x2) w: (6) #a__from(x1) w: (4) #a__quot(x1,x2) w: (4) minus(x1,x2) w: (2) a__from(x1) w: (26817) a__zWquot(x1,x2) w: (1 + x1) zWquot(x1,x2) w: (978 + x2 + x1) a__quot(x1,x2) w: (1 + x1) #mark(x1) w: (x1) 0() w: (32530) quot(x1,x2) w: (2 + x1) from(x1) w: (26818 + x1) sel(x1,x2) w: (2) #a__minus(x1,x2) w: (0) nil() w: (9645) #a__sel(x1,x2) w: (0) mark(x1) w: (2) a__sel(x1,x2) w: (1) cons(x1,x2) w: (3 + x2) USABLE RULES: { } Removed DPs: #24 Number of SCCs: 1, DPs: 1 SCC { #21 } Sum... Max... QLPOpS... NegMaxSum... succeeded. a__minus(x1,x2) w: (0) s(x1) w: (max{0, 2 + x1}) #a__zWquot(x1,x2) w: (0) #a__from(x1) w: (0) #a__quot(x1,x2) w: (0) minus(x1,x2) w: (0) a__from(x1) w: (max{0, 2449 + x1}) a__zWquot(x1,x2) w: (max{0, 2 + x1}) zWquot(x1,x2) w: (max{0, 2 + x1}) a__quot(x1,x2) w: (max{0, 1 + x1}) #mark(x1) w: (0) 0() w: (0) quot(x1,x2) w: (max{0, 1 + x1}) from(x1) w: (max{0, 2449 + x1}) sel(x1,x2) w: (max{0, -1 + x2 + x1}) #a__minus(x1,x2) w: (max{0, 1 + x2}) nil() w: (1) #a__sel(x1,x2) w: (max{0, x1}) mark(x1) w: (max{0, x1}) a__sel(x1,x2) w: (max{0, -1 + x2 + x1}) cons(x1,x2) w: (max{0, -2 + x2, 3 + x1}) USABLE RULES: { 1..24 } Removed DPs: #21 Number of SCCs: 0, DPs: 0