/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(and(tt(),X)) -> mark(X) 2: active(plus(N,0())) -> mark(N) 3: active(plus(N,s(M))) -> mark(s(plus(N,M))) 4: active(x(N,0())) -> mark(0()) 5: active(x(N,s(M))) -> mark(plus(x(N,M),N)) 6: active(and(X1,X2)) -> and(active(X1),X2) 7: active(plus(X1,X2)) -> plus(active(X1),X2) 8: active(plus(X1,X2)) -> plus(X1,active(X2)) 9: active(s(X)) -> s(active(X)) 10: active(x(X1,X2)) -> x(active(X1),X2) 11: active(x(X1,X2)) -> x(X1,active(X2)) 12: and(mark(X1),X2) -> mark(and(X1,X2)) 13: plus(mark(X1),X2) -> mark(plus(X1,X2)) 14: plus(X1,mark(X2)) -> mark(plus(X1,X2)) 15: s(mark(X)) -> mark(s(X)) 16: x(mark(X1),X2) -> mark(x(X1,X2)) 17: x(X1,mark(X2)) -> mark(x(X1,X2)) 18: proper(and(X1,X2)) -> and(proper(X1),proper(X2)) 19: proper(tt()) -> ok(tt()) 20: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) 21: proper(0()) -> ok(0()) 22: proper(s(X)) -> s(proper(X)) 23: proper(x(X1,X2)) -> x(proper(X1),proper(X2)) 24: and(ok(X1),ok(X2)) -> ok(and(X1,X2)) 25: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) 26: s(ok(X)) -> ok(s(X)) 27: x(ok(X1),ok(X2)) -> ok(x(X1,X2)) 28: top(mark(X)) -> top(proper(X)) 29: top(ok(X)) -> top(active(X)) Number of strict rules: 29 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #top(ok(X)) -> #top(active(X)) #2: #top(ok(X)) -> #active(X) #3: #active(and(X1,X2)) -> #and(active(X1),X2) #4: #active(and(X1,X2)) -> #active(X1) #5: #plus(mark(X1),X2) -> #plus(X1,X2) #6: #active(s(X)) -> #s(active(X)) #7: #active(s(X)) -> #active(X) #8: #active(x(X1,X2)) -> #x(X1,active(X2)) #9: #active(x(X1,X2)) -> #active(X2) #10: #and(ok(X1),ok(X2)) -> #and(X1,X2) #11: #proper(x(X1,X2)) -> #x(proper(X1),proper(X2)) #12: #proper(x(X1,X2)) -> #proper(X1) #13: #proper(x(X1,X2)) -> #proper(X2) #14: #and(mark(X1),X2) -> #and(X1,X2) #15: #plus(X1,mark(X2)) -> #plus(X1,X2) #16: #plus(ok(X1),ok(X2)) -> #plus(X1,X2) #17: #proper(plus(X1,X2)) -> #plus(proper(X1),proper(X2)) #18: #proper(plus(X1,X2)) -> #proper(X1) #19: #proper(plus(X1,X2)) -> #proper(X2) #20: #active(plus(X1,X2)) -> #plus(active(X1),X2) #21: #active(plus(X1,X2)) -> #active(X1) #22: #active(x(X1,X2)) -> #x(active(X1),X2) #23: #active(x(X1,X2)) -> #active(X1) #24: #active(x(N,s(M))) -> #plus(x(N,M),N) #25: #active(x(N,s(M))) -> #x(N,M) #26: #top(mark(X)) -> #top(proper(X)) #27: #top(mark(X)) -> #proper(X) #28: #proper(s(X)) -> #s(proper(X)) #29: #proper(s(X)) -> #proper(X) #30: #x(ok(X1),ok(X2)) -> #x(X1,X2) #31: #x(X1,mark(X2)) -> #x(X1,X2) #32: #s(ok(X)) -> #s(X) #33: #x(mark(X1),X2) -> #x(X1,X2) #34: #active(plus(N,s(M))) -> #s(plus(N,M)) #35: #active(plus(N,s(M))) -> #plus(N,M) #36: #active(plus(X1,X2)) -> #plus(X1,active(X2)) #37: #active(plus(X1,X2)) -> #active(X2) #38: #s(mark(X)) -> #s(X) #39: #proper(and(X1,X2)) -> #and(proper(X1),proper(X2)) #40: #proper(and(X1,X2)) -> #proper(X1) #41: #proper(and(X1,X2)) -> #proper(X2) Number of SCCs: 7, DPs: 25 SCC { #32 #38 } POLO(Sum)... succeeded. s w: 0 top w: 0 and w: 0 #plus w: 0 #top w: 0 x w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #x w: 0 #s w: x1 mark w: x1 + 1 #proper w: 0 plus w: 0 active w: 0 #active w: 0 tt w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #32 #38 Number of SCCs: 6, DPs: 23 SCC { #1 #26 } POLO(Sum)... POLO(max)... QLPOS... succeeded. s s: [1] p: 2 top s: [] p: 0 and s: [1,2] p: 3 #plus s: [1,2] p: 0 #top s: [1] p: 0 x s: [1,2] p: 4 proper s: 1 ok s: 1 0 s: [] p: 1 #x s: [1,2] p: 0 #s s: [] p: 0 mark s: [1] p: 2 #proper s: [] p: 0 plus s: [1,2] p: 3 active s: 1 #active s: [] p: 0 tt s: [] p: 1 #and s: [2,1] p: 0 USABLE RULES: { 1..27 } Removed DPs: #26 Number of SCCs: 6, DPs: 22 SCC { #1 } POLO(Sum)... succeeded. s w: x1 top w: 0 and w: x1 #plus w: 0 #top w: x1 x w: x2 proper w: 3 ok w: x1 + 2 0 w: 1 #x w: 0 #s w: 0 mark w: 0 #proper w: 0 plus w: x1 active w: x1 + 1 #active w: 0 tt w: 1 #and w: 0 USABLE RULES: { 1..27 } Removed DPs: #1 Number of SCCs: 5, DPs: 21 SCC { #10 #14 } POLO(Sum)... succeeded. s w: x1 top w: 0 and w: x1 #plus w: 0 #top w: x1 x w: x2 proper w: 3 ok w: x1 + 2 0 w: 1 #x w: 0 #s w: 0 mark w: 0 #proper w: 0 plus w: x1 active w: x1 + 1 #active w: 0 tt w: 1 #and w: x2 USABLE RULES: { 1..27 } Removed DPs: #10 Number of SCCs: 5, DPs: 20 SCC { #14 } POLO(Sum)... succeeded. s w: x1 top w: 0 and w: x1 #plus w: 0 #top w: 0 x w: x2 proper w: 3 ok w: x1 + 2 0 w: 1 #x w: 0 #s w: 0 mark w: x1 + 1 #proper w: 0 plus w: x1 active w: x1 + 1 #active w: 0 tt w: 1 #and w: x1 USABLE RULES: { 2 4 12 15 19 21 24 26 } Removed DPs: #14 Number of SCCs: 4, DPs: 19 SCC { #30 #31 #33 } POLO(Sum)... succeeded. s w: x1 top w: 0 and w: x1 #plus w: 0 #top w: 0 x w: x2 proper w: 3 ok w: x1 + 2 0 w: 1 #x w: x1 + x2 #s w: 0 mark w: x1 + 1 #proper w: 0 plus w: x1 active w: x1 + 1 #active w: 0 tt w: 1 #and w: 0 USABLE RULES: { 2 4 12 15 19 21 24 26 } Removed DPs: #30 #31 #33 Number of SCCs: 3, DPs: 16 SCC { #5 #15 #16 } POLO(Sum)... succeeded. s w: x1 top w: 0 and w: x1 #plus w: x1 + x2 #top w: 0 x w: x2 proper w: 3 ok w: x1 + 2 0 w: 1 #x w: 0 #s w: 0 mark w: x1 + 1 #proper w: 0 plus w: x1 active w: x1 + 1 #active w: 0 tt w: 1 #and w: 0 USABLE RULES: { 2 4 12 15 19 21 24 26 } Removed DPs: #5 #15 #16 Number of SCCs: 2, DPs: 13 SCC { #4 #7 #9 #21 #23 #37 } POLO(Sum)... succeeded. s w: x1 + 1 top w: 0 and w: x1 + 1 #plus w: 0 #top w: 0 x w: x1 + x2 + 1 proper w: 3 ok w: x1 + 2 0 w: 1 #x w: 0 #s w: 0 mark w: 1 #proper w: 0 plus w: x1 + x2 + 1 active w: 1 #active w: x1 tt w: 1 #and w: 0 USABLE RULES: { 2 4 12..17 19 21 24 26 27 } Removed DPs: #4 #7 #9 #21 #23 #37 Number of SCCs: 1, DPs: 7 SCC { #12 #13 #18 #19 #29 #40 #41 } POLO(Sum)... succeeded. s w: x1 + 1 top w: 0 and w: x1 + x2 + 1 #plus w: 0 #top w: 0 x w: x1 + x2 + 1 proper w: 2 ok w: x1 + 1 0 w: 1 #x w: 0 #s w: 0 mark w: 1 #proper w: x1 plus w: x1 + x2 + 1 active w: 1 #active w: 0 tt w: 1 #and w: 0 USABLE RULES: { 2 4 12..17 19 21 24 26 27 } Removed DPs: #12 #13 #18 #19 #29 #40 #41 Number of SCCs: 0, DPs: 0