/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(sel(0(),cons(X,XS))) -> mark(X) 3: active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) 4: active(minus(X,0())) -> mark(0()) 5: active(minus(s(X),s(Y))) -> mark(minus(X,Y)) 6: active(quot(0(),s(Y))) -> mark(0()) 7: active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) 8: active(zWquot(XS,nil())) -> mark(nil()) 9: active(zWquot(nil(),XS)) -> mark(nil()) 10: active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) 11: mark(from(X)) -> active(from(mark(X))) 12: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) 13: mark(s(X)) -> active(s(mark(X))) 14: mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2))) 15: mark(0()) -> active(0()) 16: mark(minus(X1,X2)) -> active(minus(mark(X1),mark(X2))) 17: mark(quot(X1,X2)) -> active(quot(mark(X1),mark(X2))) 18: mark(zWquot(X1,X2)) -> active(zWquot(mark(X1),mark(X2))) 19: mark(nil()) -> active(nil()) 20: from(mark(X)) -> from(X) 21: from(active(X)) -> from(X) 22: cons(mark(X1),X2) -> cons(X1,X2) 23: cons(X1,mark(X2)) -> cons(X1,X2) 24: cons(active(X1),X2) -> cons(X1,X2) 25: cons(X1,active(X2)) -> cons(X1,X2) 26: s(mark(X)) -> s(X) 27: s(active(X)) -> s(X) 28: sel(mark(X1),X2) -> sel(X1,X2) 29: sel(X1,mark(X2)) -> sel(X1,X2) 30: sel(active(X1),X2) -> sel(X1,X2) 31: sel(X1,active(X2)) -> sel(X1,X2) 32: minus(mark(X1),X2) -> minus(X1,X2) 33: minus(X1,mark(X2)) -> minus(X1,X2) 34: minus(active(X1),X2) -> minus(X1,X2) 35: minus(X1,active(X2)) -> minus(X1,X2) 36: quot(mark(X1),X2) -> quot(X1,X2) 37: quot(X1,mark(X2)) -> quot(X1,X2) 38: quot(active(X1),X2) -> quot(X1,X2) 39: quot(X1,active(X2)) -> quot(X1,X2) 40: zWquot(mark(X1),X2) -> zWquot(X1,X2) 41: zWquot(X1,mark(X2)) -> zWquot(X1,X2) 42: zWquot(active(X1),X2) -> zWquot(X1,X2) 43: zWquot(X1,active(X2)) -> zWquot(X1,X2) Number of strict rules: 43 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #active(sel(0(),cons(X,XS))) -> #mark(X) #2: #zWquot(X1,active(X2)) -> #zWquot(X1,X2) #3: #sel(X1,mark(X2)) -> #sel(X1,X2) #4: #minus(X1,active(X2)) -> #minus(X1,X2) #5: #zWquot(active(X1),X2) -> #zWquot(X1,X2) #6: #zWquot(X1,mark(X2)) -> #zWquot(X1,X2) #7: #quot(X1,mark(X2)) -> #quot(X1,X2) #8: #quot(active(X1),X2) -> #quot(X1,X2) #9: #active(quot(0(),s(Y))) -> #mark(0()) #10: #zWquot(mark(X1),X2) -> #zWquot(X1,X2) #11: #mark(s(X)) -> #active(s(mark(X))) #12: #mark(s(X)) -> #s(mark(X)) #13: #mark(s(X)) -> #mark(X) #14: #active(zWquot(nil(),XS)) -> #mark(nil()) #15: #mark(from(X)) -> #active(from(mark(X))) #16: #mark(from(X)) -> #from(mark(X)) #17: #mark(from(X)) -> #mark(X) #18: #cons(active(X1),X2) -> #cons(X1,X2) #19: #cons(X1,mark(X2)) -> #cons(X1,X2) #20: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2)) #21: #mark(cons(X1,X2)) -> #cons(mark(X1),X2) #22: #mark(cons(X1,X2)) -> #mark(X1) #23: #sel(X1,active(X2)) -> #sel(X1,X2) #24: #mark(sel(X1,X2)) -> #active(sel(mark(X1),mark(X2))) #25: #mark(sel(X1,X2)) -> #sel(mark(X1),mark(X2)) #26: #mark(sel(X1,X2)) -> #mark(X1) #27: #mark(sel(X1,X2)) -> #mark(X2) #28: #sel(active(X1),X2) -> #sel(X1,X2) #29: #cons(X1,active(X2)) -> #cons(X1,X2) #30: #from(mark(X)) -> #from(X) #31: #active(quot(s(X),s(Y))) -> #mark(s(quot(minus(X,Y),s(Y)))) #32: #active(quot(s(X),s(Y))) -> #s(quot(minus(X,Y),s(Y))) #33: #active(quot(s(X),s(Y))) -> #quot(minus(X,Y),s(Y)) #34: #active(quot(s(X),s(Y))) -> #minus(X,Y) #35: #quot(X1,active(X2)) -> #quot(X1,X2) #36: #active(zWquot(cons(X,XS),cons(Y,YS))) -> #mark(cons(quot(X,Y),zWquot(XS,YS))) #37: #active(zWquot(cons(X,XS),cons(Y,YS))) -> #cons(quot(X,Y),zWquot(XS,YS)) #38: #active(zWquot(cons(X,XS),cons(Y,YS))) -> #quot(X,Y) #39: #active(zWquot(cons(X,XS),cons(Y,YS))) -> #zWquot(XS,YS) #40: #minus(X1,mark(X2)) -> #minus(X1,X2) #41: #active(minus(s(X),s(Y))) -> #mark(minus(X,Y)) #42: #active(minus(s(X),s(Y))) -> #minus(X,Y) #43: #sel(mark(X1),X2) -> #sel(X1,X2) #44: #cons(mark(X1),X2) -> #cons(X1,X2) #45: #minus(active(X1),X2) -> #minus(X1,X2) #46: #s(active(X)) -> #s(X) #47: #mark(quot(X1,X2)) -> #active(quot(mark(X1),mark(X2))) #48: #mark(quot(X1,X2)) -> #quot(mark(X1),mark(X2)) #49: #mark(quot(X1,X2)) -> #mark(X1) #50: #mark(quot(X1,X2)) -> #mark(X2) #51: #minus(mark(X1),X2) -> #minus(X1,X2) #52: #mark(nil()) -> #active(nil()) #53: #s(mark(X)) -> #s(X) #54: #quot(mark(X1),X2) -> #quot(X1,X2) #55: #from(active(X)) -> #from(X) #56: #mark(minus(X1,X2)) -> #active(minus(mark(X1),mark(X2))) #57: #mark(minus(X1,X2)) -> #minus(mark(X1),mark(X2)) #58: #mark(minus(X1,X2)) -> #mark(X1) #59: #mark(minus(X1,X2)) -> #mark(X2) #60: #active(sel(s(N),cons(X,XS))) -> #mark(sel(N,XS)) #61: #active(sel(s(N),cons(X,XS))) -> #sel(N,XS) #62: #active(from(X)) -> #mark(cons(X,from(s(X)))) #63: #active(from(X)) -> #cons(X,from(s(X))) #64: #active(from(X)) -> #from(s(X)) #65: #active(from(X)) -> #s(X) #66: #active(zWquot(XS,nil())) -> #mark(nil()) #67: #mark(0()) -> #active(0()) #68: #active(minus(X,0())) -> #mark(0()) #69: #mark(zWquot(X1,X2)) -> #active(zWquot(mark(X1),mark(X2))) #70: #mark(zWquot(X1,X2)) -> #zWquot(mark(X1),mark(X2)) #71: #mark(zWquot(X1,X2)) -> #mark(X1) #72: #mark(zWquot(X1,X2)) -> #mark(X2) Number of SCCs: 8, DPs: 46 SCC { #30 #55 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #zWquot w: 0 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: 0 #from w: x1 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #30 #55 Number of SCCs: 7, DPs: 44 SCC { #46 #53 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #zWquot w: 0 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 #s w: x1 nil w: 0 mark w: x1 + 1 #minus w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #46 #53 Number of SCCs: 6, DPs: 42 SCC { #4 #40 #45 #51 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #zWquot w: 0 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: x1 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #45 #51 Number of SCCs: 6, DPs: 40 SCC { #4 #40 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #zWquot w: 0 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: x2 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #4 #40 Number of SCCs: 5, DPs: 38 SCC { #7 #8 #35 #54 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #zWquot w: 0 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: x1 USABLE RULES: { } Removed DPs: #8 #54 Number of SCCs: 5, DPs: 36 SCC { #7 #35 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #zWquot w: 0 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: x2 USABLE RULES: { } Removed DPs: #7 #35 Number of SCCs: 4, DPs: 34 SCC { #18 #19 #29 #44 } POLO(Sum)... succeeded. #cons w: x1 s w: 0 #zWquot w: 0 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #18 #44 Number of SCCs: 4, DPs: 32 SCC { #19 #29 } POLO(Sum)... succeeded. #cons w: x2 s w: 0 #zWquot w: 0 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #19 #29 Number of SCCs: 3, DPs: 30 SCC { #3 #23 #28 #43 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #zWquot w: 0 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: x2 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #3 #23 Number of SCCs: 3, DPs: 28 SCC { #28 #43 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #zWquot w: 0 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: x1 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #28 #43 Number of SCCs: 2, DPs: 26 SCC { #2 #5 #6 #10 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #zWquot w: x1 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #5 #10 Number of SCCs: 2, DPs: 24 SCC { #2 #6 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #zWquot w: x2 minus w: 0 zWquot w: 0 #mark w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 #minus w: 0 #from w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #2 #6 Number of SCCs: 1, DPs: 22 SCC { #1 #13 #15 #17 #22 #24 #26 #27 #31 #36 #41 #47 #49 #50 #56 #58..60 #62 #69 #71 #72 } POLO(Sum)... POLO(max)... succeeded. #cons w: 0 s w: x1 #zWquot w: 0 minus w: max(x1, x2 + 1) zWquot w: max(x1 + 3, x2 + 2) #mark w: x1 0 w: 3 quot w: max(x1 + 1, x2 + 2) #sel w: 0 from w: x1 + 1 sel w: max(x1 + 1, x2 + 2) #s w: 0 nil w: 4 mark w: x1 #minus w: 0 #from w: 0 active w: x1 cons w: max(x1, x2) #active w: x1 #quot w: 0 USABLE RULES: { 1..43 } Removed DPs: #1 #17 #26 #27 #49 #50 #59 #71 #72 Number of SCCs: 2, DPs: 13 SCC { #24 #60 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #cons s: [2,1] p: 0 w: max(x1 + 1, x2) s s: [1] p: 1 w: x1 #zWquot s: [] p: 0 w: 1 minus s: [] p: 1 w: max(x1) zWquot s: [2] p: 3 w: x1 + x2 + 4 #mark s: [1] p: 0 w: x1 0 s: [] p: 1 w: 0 quot s: [1] p: 2 w: max(x1 + 2, x2) #sel s: [1,2] p: 0 w: x1 + x2 from s: [1] p: 3 w: x1 + 4 sel s: [1] p: 2 w: x1 + x2 + 1 #s s: [] p: 0 w: 0 nil s: [] p: 0 w: 0 mark s: 1 #minus s: [] p: 0 w: max(x1) #from s: [] p: 0 w: 0 active s: 1 cons s: [] p: 3 w: max(x1 + 3, x2) #active s: [1] p: 0 w: x1 #quot s: [] p: 0 w: 0 USABLE RULES: { 1..43 } Removed DPs: #60 Number of SCCs: 1, DPs: 11 SCC { #13 #15 #22 #31 #36 #41 #47 #56 #58 #62 #69 } POLO(Sum)... POLO(max)... succeeded. #cons w: 0 s w: x1 #zWquot w: 0 minus w: max(x1 + 1, x2 + 2) zWquot w: max(x1 + 3, x2 + 4) #mark w: x1 + 1 0 w: 0 quot w: 0 #sel w: 0 from w: x1 + 3 sel w: max(x2 + 1) #s w: 0 nil w: 0 mark w: x1 #minus w: 0 #from w: 0 active w: x1 cons w: max(x1 + 2, x2) #active w: x1 + 1 #quot w: 0 USABLE RULES: { 1..43 } Removed DPs: #22 #58 Number of SCCs: 2, DPs: 5 SCC { #41 #56 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. #cons w: 0 s w: max(x1 + 4, 0) #zWquot w: 0 minus w: max(x1 - 2, 0) zWquot w: max(x1 + 4, 0) #mark w: max(x1 + 4, 0) 0 w: 0 quot w: max(x1 + 4, 0) #sel w: max(x2 - 1, 0) from w: max(x1 + 5, 0) sel w: max(x1 + x2 - 4, 0) #s w: 0 nil w: 1 mark w: max(x1, 0) #minus w: 0 #from w: max(x1 - 1, 0) active w: max(x1, 0) cons w: max(x1 + 5, x2 - 4, 0) #active w: max(x1 + 3, 0) #quot w: 0 USABLE RULES: { 1..43 } Removed DPs: #41 #56 Number of SCCs: 1, DPs: 3 SCC { #13 #31 #47 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. #cons w: 0 s w: max(x1 + 5, 0) #zWquot w: 0 minus w: max(x1 - 3, 0) zWquot w: max(x1 + 5, 0) #mark w: max(x1 + 3, 0) 0 w: 0 quot w: max(x1 + 5, 0) #sel w: max(x2 - 1, 0) from w: max(x1 + 6, 0) sel w: max(x1 + x2 - 5, 0) #s w: 0 nil w: 1 mark w: max(x1, 0) #minus w: 0 #from w: max(x1 - 1, 0) active w: max(x1, 0) cons w: max(x1 + 6, x2 - 5, 0) #active w: max(x1 + 3, 0) #quot w: 0 USABLE RULES: { 1..43 } Removed DPs: #13 Number of SCCs: 0, DPs: 0