/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: active(f(X)) -> mark(cons(X,f(g(X)))) 2: active(g(0())) -> mark(s(0())) 3: active(g(s(X))) -> mark(s(s(g(X)))) 4: active(sel(0(),cons(X,Y))) -> mark(X) 5: active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) 6: active(f(X)) -> f(active(X)) 7: active(cons(X1,X2)) -> cons(active(X1),X2) 8: active(g(X)) -> g(active(X)) 9: active(s(X)) -> s(active(X)) 10: active(sel(X1,X2)) -> sel(active(X1),X2) 11: active(sel(X1,X2)) -> sel(X1,active(X2)) 12: f(mark(X)) -> mark(f(X)) 13: cons(mark(X1),X2) -> mark(cons(X1,X2)) 14: g(mark(X)) -> mark(g(X)) 15: s(mark(X)) -> mark(s(X)) 16: sel(mark(X1),X2) -> mark(sel(X1,X2)) 17: sel(X1,mark(X2)) -> mark(sel(X1,X2)) 18: proper(f(X)) -> f(proper(X)) 19: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 20: proper(g(X)) -> g(proper(X)) 21: proper(0()) -> ok(0()) 22: proper(s(X)) -> s(proper(X)) 23: proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) 24: f(ok(X)) -> ok(f(X)) 25: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 26: g(ok(X)) -> ok(g(X)) 27: s(ok(X)) -> ok(s(X)) 28: sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) 29: top(mark(X)) -> top(proper(X)) 30: top(ok(X)) -> top(active(X)) Number of strict rules: 30 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #active(g(0())) -> #s(0()) #2: #top(mark(X)) -> #top(proper(X)) #3: #top(mark(X)) -> #proper(X) #4: #active(f(X)) -> #f(active(X)) #5: #active(f(X)) -> #active(X) #6: #cons(mark(X1),X2) -> #cons(X1,X2) #7: #active(s(X)) -> #s(active(X)) #8: #active(s(X)) -> #active(X) #9: #active(sel(X1,X2)) -> #sel(X1,active(X2)) #10: #active(sel(X1,X2)) -> #active(X2) #11: #f(ok(X)) -> #f(X) #12: #proper(sel(X1,X2)) -> #sel(proper(X1),proper(X2)) #13: #proper(sel(X1,X2)) -> #proper(X1) #14: #proper(sel(X1,X2)) -> #proper(X2) #15: #f(mark(X)) -> #f(X) #16: #g(mark(X)) -> #g(X) #17: #top(ok(X)) -> #top(active(X)) #18: #top(ok(X)) -> #active(X) #19: #cons(ok(X1),ok(X2)) -> #cons(X1,X2) #20: #proper(g(X)) -> #g(proper(X)) #21: #proper(g(X)) -> #proper(X) #22: #active(cons(X1,X2)) -> #cons(active(X1),X2) #23: #active(cons(X1,X2)) -> #active(X1) #24: #active(sel(X1,X2)) -> #sel(active(X1),X2) #25: #active(sel(X1,X2)) -> #active(X1) #26: #active(sel(s(X),cons(Y,Z))) -> #sel(X,Z) #27: #sel(ok(X1),ok(X2)) -> #sel(X1,X2) #28: #proper(s(X)) -> #s(proper(X)) #29: #proper(s(X)) -> #proper(X) #30: #s(ok(X)) -> #s(X) #31: #sel(X1,mark(X2)) -> #sel(X1,X2) #32: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2)) #33: #proper(cons(X1,X2)) -> #proper(X1) #34: #proper(cons(X1,X2)) -> #proper(X2) #35: #g(ok(X)) -> #g(X) #36: #sel(mark(X1),X2) -> #sel(X1,X2) #37: #active(g(s(X))) -> #s(s(g(X))) #38: #active(g(s(X))) -> #s(g(X)) #39: #active(g(s(X))) -> #g(X) #40: #active(f(X)) -> #cons(X,f(g(X))) #41: #active(f(X)) -> #f(g(X)) #42: #active(f(X)) -> #g(X) #43: #active(g(X)) -> #g(active(X)) #44: #active(g(X)) -> #active(X) #45: #s(mark(X)) -> #s(X) #46: #proper(f(X)) -> #f(proper(X)) #47: #proper(f(X)) -> #proper(X) Number of SCCs: 8, DPs: 26 SCC { #30 #45 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 top w: 0 #top w: 0 f w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #sel w: 0 sel w: 0 #s w: x1 mark w: x1 + 1 #f w: 0 #g w: 0 #proper w: 0 active w: 0 cons w: 0 #active w: 0 g w: 0 USABLE RULES: { } Removed DPs: #30 #45 Number of SCCs: 7, DPs: 24 SCC { #11 #15 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 top w: 0 #top w: 0 f w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #sel w: 0 sel w: 0 #s w: 0 mark w: x1 + 1 #f w: x1 #g w: 0 #proper w: 0 active w: 0 cons w: 0 #active w: 0 g w: 0 USABLE RULES: { } Removed DPs: #11 #15 Number of SCCs: 6, DPs: 22 SCC { #16 #35 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 top w: 0 #top w: 0 f w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #sel w: 0 sel w: 0 #s w: 0 mark w: x1 + 1 #f w: 0 #g w: x1 #proper w: 0 active w: 0 cons w: 0 #active w: 0 g w: 0 USABLE RULES: { } Removed DPs: #16 #35 Number of SCCs: 5, DPs: 20 SCC { #2 #17 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #cons s: [] p: 0 w: max(x1 + 1) s s: [1] p: 1 w: x1 top s: [] p: 0 w: 0 #top s: [1] p: 0 w: x1 + 1 f s: [1] p: 4 w: x1 + 2 proper s: 1 ok s: 1 0 s: [] p: 4 w: 1 #sel s: [1] p: 0 w: x1 sel s: [1,2] p: 4 w: x1 + x2 + 2 #s s: [] p: 0 w: 0 mark s: [1] p: 1 w: x1 #f s: [] p: 0 w: 0 #g s: [] p: 0 w: 0 #proper s: [] p: 0 w: 0 active s: 1 cons s: [1] p: 2 w: max(x1 + 1, x2) #active s: [] p: 0 w: 0 g s: [1] p: 5 w: x1 USABLE RULES: { 1..28 } Removed DPs: #2 Number of SCCs: 5, DPs: 19 SCC { #17 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 top w: 0 #top w: x1 f w: x1 proper w: 3 ok w: x1 + 2 0 w: 1 #sel w: 0 sel w: x1 #s w: 0 mark w: 0 #f w: 0 #g w: 0 #proper w: 0 active w: x1 + 1 cons w: x1 #active w: 0 g w: x1 USABLE RULES: { 1..28 } Removed DPs: #17 Number of SCCs: 4, DPs: 18 SCC { #6 #19 } POLO(Sum)... succeeded. #cons w: x2 s w: x1 top w: 0 #top w: x1 f w: x1 proper w: 3 ok w: x1 + 2 0 w: 1 #sel w: 0 sel w: x1 #s w: 0 mark w: 0 #f w: 0 #g w: 0 #proper w: 0 active w: x1 + 1 cons w: x1 #active w: 0 g w: x1 USABLE RULES: { 1..28 } Removed DPs: #19 Number of SCCs: 4, DPs: 17 SCC { #6 } POLO(Sum)... succeeded. #cons w: x1 s w: x1 top w: 0 #top w: 0 f w: x1 proper w: 3 ok w: x1 + 2 0 w: 2 #sel w: 0 sel w: x1 + x2 #s w: 0 mark w: x1 + 1 #f w: 0 #g w: 0 #proper w: 0 active w: x1 + 2 cons w: x1 #active w: 0 g w: x1 USABLE RULES: { 2 3 12..17 24..28 } Removed DPs: #6 Number of SCCs: 3, DPs: 16 SCC { #27 #31 #36 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 top w: 0 #top w: 0 f w: x1 proper w: 3 ok w: x1 + 2 0 w: 2 #sel w: x1 + x2 sel w: x1 + x2 #s w: 0 mark w: x1 + 1 #f w: 0 #g w: 0 #proper w: 0 active w: x1 + 2 cons w: x1 #active w: 0 g w: x1 USABLE RULES: { 2 3 12..17 24..28 } Removed DPs: #27 #31 #36 Number of SCCs: 2, DPs: 13 SCC { #5 #8 #10 #23 #25 #44 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 + 1 top w: 0 #top w: 0 f w: x1 + 1 proper w: 1 ok w: x1 + 1 0 w: 1 #sel w: 0 sel w: x1 + x2 #s w: 0 mark w: 1 #f w: 0 #g w: 0 #proper w: 0 active w: 2 cons w: x1 + x2 + 1 #active w: x1 g w: x1 + 1 USABLE RULES: { 2 3 12..17 24..28 } Removed DPs: #5 #8 #23 #44 Number of SCCs: 2, DPs: 9 SCC { #10 #25 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 + 1 top w: 0 #top w: 0 f w: 2 proper w: 1 ok w: x1 0 w: 2 #sel w: 0 sel w: x1 + x2 + 1 #s w: 0 mark w: 1 #f w: 0 #g w: 0 #proper w: 0 active w: x1 + 2 cons w: x1 + x2 + 1 #active w: x1 g w: x1 + 1 USABLE RULES: { 1..17 24..28 } Removed DPs: #10 #25 Number of SCCs: 1, DPs: 7 SCC { #13 #14 #21 #29 #33 #34 #47 } POLO(Sum)... succeeded. #cons w: 0 s w: x1 + 1 top w: 0 #top w: 0 f w: x1 + 1 proper w: 1 ok w: x1 0 w: 2 #sel w: 0 sel w: x1 + x2 + 1 #s w: 0 mark w: 5 #f w: 0 #g w: 0 #proper w: x1 active w: x1 + 1 cons w: x1 + x2 + 1 #active w: 0 g w: x1 + 3 USABLE RULES: { 16 17 28 } Removed DPs: #13 #14 #21 #29 #33 #34 #47 Number of SCCs: 0, DPs: 0