/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE Input TRS: 1: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) 2: active(U12(tt())) -> mark(tt()) 3: active(U21(tt())) -> mark(tt()) 4: active(U31(tt(),N)) -> mark(N) 5: active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) 6: active(U42(tt(),M,N)) -> mark(s(plus(N,M))) 7: active(isNat(0())) -> mark(tt()) 8: active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) 9: active(isNat(s(V1))) -> mark(U21(isNat(V1))) 10: active(plus(N,0())) -> mark(U31(isNat(N),N)) 11: active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) 12: active(U11(X1,X2)) -> U11(active(X1),X2) 13: active(U12(X)) -> U12(active(X)) 14: active(U21(X)) -> U21(active(X)) 15: active(U31(X1,X2)) -> U31(active(X1),X2) 16: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) 17: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) 18: active(s(X)) -> s(active(X)) 19: active(plus(X1,X2)) -> plus(active(X1),X2) 20: active(plus(X1,X2)) -> plus(X1,active(X2)) 21: U11(mark(X1),X2) -> mark(U11(X1,X2)) 22: U12(mark(X)) -> mark(U12(X)) 23: U21(mark(X)) -> mark(U21(X)) 24: U31(mark(X1),X2) -> mark(U31(X1,X2)) 25: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) 26: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) 27: s(mark(X)) -> mark(s(X)) 28: plus(mark(X1),X2) -> mark(plus(X1,X2)) 29: plus(X1,mark(X2)) -> mark(plus(X1,X2)) 30: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) 31: proper(tt()) -> ok(tt()) 32: proper(U12(X)) -> U12(proper(X)) 33: proper(isNat(X)) -> isNat(proper(X)) 34: proper(U21(X)) -> U21(proper(X)) 35: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) 36: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) 37: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) 38: proper(s(X)) -> s(proper(X)) 39: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) 40: proper(0()) -> ok(0()) 41: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) 42: U12(ok(X)) -> ok(U12(X)) 43: isNat(ok(X)) -> ok(isNat(X)) 44: U21(ok(X)) -> ok(U21(X)) 45: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) 46: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) 47: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) 48: s(ok(X)) -> ok(s(X)) 49: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) 50: top(mark(X)) -> top(proper(X)) 51: top(ok(X)) -> top(active(X)) Number of strict rules: 51 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #isNat(ok(X)) -> #isNat(X) #2: #plus(X1,mark(X2)) -> #plus(X1,X2) #3: #proper(U31(X1,X2)) -> #U31(proper(X1),proper(X2)) #4: #proper(U31(X1,X2)) -> #proper(X1) #5: #proper(U31(X1,X2)) -> #proper(X2) #6: #U41(ok(X1),ok(X2),ok(X3)) -> #U41(X1,X2,X3) #7: #U12(ok(X)) -> #U12(X) #8: #U11(ok(X1),ok(X2)) -> #U11(X1,X2) #9: #proper(U42(X1,X2,X3)) -> #U42(proper(X1),proper(X2),proper(X3)) #10: #proper(U42(X1,X2,X3)) -> #proper(X1) #11: #proper(U42(X1,X2,X3)) -> #proper(X2) #12: #proper(U42(X1,X2,X3)) -> #proper(X3) #13: #U42(ok(X1),ok(X2),ok(X3)) -> #U42(X1,X2,X3) #14: #s(ok(X)) -> #s(X) #15: #proper(s(X)) -> #s(proper(X)) #16: #proper(s(X)) -> #proper(X) #17: #active(U42(tt(),M,N)) -> #s(plus(N,M)) #18: #active(U42(tt(),M,N)) -> #plus(N,M) #19: #top(ok(X)) -> #top(active(X)) #20: #top(ok(X)) -> #active(X) #21: #active(U12(X)) -> #U12(active(X)) #22: #active(U12(X)) -> #active(X) #23: #active(isNat(s(V1))) -> #U21(isNat(V1)) #24: #active(isNat(s(V1))) -> #isNat(V1) #25: #active(plus(N,s(M))) -> #U41(isNat(M),M,N) #26: #active(plus(N,s(M))) -> #isNat(M) #27: #U31(mark(X1),X2) -> #U31(X1,X2) #28: #U21(mark(X)) -> #U21(X) #29: #U31(ok(X1),ok(X2)) -> #U31(X1,X2) #30: #active(U11(X1,X2)) -> #U11(active(X1),X2) #31: #active(U11(X1,X2)) -> #active(X1) #32: #active(U21(X)) -> #U21(active(X)) #33: #active(U21(X)) -> #active(X) #34: #proper(U11(X1,X2)) -> #U11(proper(X1),proper(X2)) #35: #proper(U11(X1,X2)) -> #proper(X1) #36: #proper(U11(X1,X2)) -> #proper(X2) #37: #plus(ok(X1),ok(X2)) -> #plus(X1,X2) #38: #U41(mark(X1),X2,X3) -> #U41(X1,X2,X3) #39: #active(plus(X1,X2)) -> #plus(X1,active(X2)) #40: #active(plus(X1,X2)) -> #active(X2) #41: #proper(plus(X1,X2)) -> #plus(proper(X1),proper(X2)) #42: #proper(plus(X1,X2)) -> #proper(X1) #43: #proper(plus(X1,X2)) -> #proper(X2) #44: #active(plus(N,0())) -> #U31(isNat(N),N) #45: #active(plus(N,0())) -> #isNat(N) #46: #proper(isNat(X)) -> #isNat(proper(X)) #47: #proper(isNat(X)) -> #proper(X) #48: #active(U41(tt(),M,N)) -> #U42(isNat(N),M,N) #49: #active(U41(tt(),M,N)) -> #isNat(N) #50: #U21(ok(X)) -> #U21(X) #51: #plus(mark(X1),X2) -> #plus(X1,X2) #52: #U12(mark(X)) -> #U12(X) #53: #proper(U21(X)) -> #U21(proper(X)) #54: #proper(U21(X)) -> #proper(X) #55: #s(mark(X)) -> #s(X) #56: #active(U42(X1,X2,X3)) -> #U42(active(X1),X2,X3) #57: #active(U42(X1,X2,X3)) -> #active(X1) #58: #proper(U12(X)) -> #U12(proper(X)) #59: #proper(U12(X)) -> #proper(X) #60: #active(plus(X1,X2)) -> #plus(active(X1),X2) #61: #active(plus(X1,X2)) -> #active(X1) #62: #U42(mark(X1),X2,X3) -> #U42(X1,X2,X3) #63: #proper(U41(X1,X2,X3)) -> #U41(proper(X1),proper(X2),proper(X3)) #64: #proper(U41(X1,X2,X3)) -> #proper(X1) #65: #proper(U41(X1,X2,X3)) -> #proper(X2) #66: #proper(U41(X1,X2,X3)) -> #proper(X3) #67: #U11(mark(X1),X2) -> #U11(X1,X2) #68: #active(U41(X1,X2,X3)) -> #U41(active(X1),X2,X3) #69: #active(U41(X1,X2,X3)) -> #active(X1) #70: #active(U11(tt(),V2)) -> #U12(isNat(V2)) #71: #active(U11(tt(),V2)) -> #isNat(V2) #72: #active(isNat(plus(V1,V2))) -> #U11(isNat(V1),V2) #73: #active(isNat(plus(V1,V2))) -> #isNat(V1) #74: #active(U31(X1,X2)) -> #U31(active(X1),X2) #75: #active(U31(X1,X2)) -> #active(X1) #76: #top(mark(X)) -> #top(proper(X)) #77: #top(mark(X)) -> #proper(X) #78: #active(s(X)) -> #s(active(X)) #79: #active(s(X)) -> #active(X) Number of SCCs: 12, DPs: 45 SCC { #1 } POLO(Sum)... succeeded. U21 w: 0 U11 w: 0 s w: 0 #isNat w: x1 U42 w: 0 top w: 0 #plus w: 0 #top w: 0 U12 w: 0 #U42 w: 0 #U12 w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: 0 mark w: 0 #proper w: 0 isNat w: 0 plus w: 0 #U11 w: 0 active w: 0 U31 w: 0 #U41 w: 0 #active w: 0 #U21 w: 0 tt w: 0 U41 w: 0 #U31 w: 0 USABLE RULES: { } Removed DPs: #1 Number of SCCs: 11, DPs: 44 SCC { #28 #50 } POLO(Sum)... succeeded. U21 w: 0 U11 w: 0 s w: 0 #isNat w: 0 U42 w: 0 top w: 0 #plus w: 0 #top w: 0 U12 w: 0 #U42 w: 0 #U12 w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 0 plus w: 0 #U11 w: 0 active w: 0 U31 w: 0 #U41 w: 0 #active w: 0 #U21 w: x1 tt w: 0 U41 w: 0 #U31 w: 0 USABLE RULES: { } Removed DPs: #28 #50 Number of SCCs: 10, DPs: 42 SCC { #7 #52 } POLO(Sum)... succeeded. U21 w: 0 U11 w: 0 s w: 0 #isNat w: 0 U42 w: 0 top w: 0 #plus w: 0 #top w: 0 U12 w: 0 #U42 w: 0 #U12 w: x1 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: 0 mark w: x1 + 1 #proper w: 0 isNat w: 0 plus w: 0 #U11 w: 0 active w: 0 U31 w: 0 #U41 w: 0 #active w: 0 #U21 w: 0 tt w: 0 U41 w: 0 #U31 w: 0 USABLE RULES: { } Removed DPs: #7 #52 Number of SCCs: 9, DPs: 40 SCC { #14 #55 } POLO(Sum)... succeeded. U21 w: 0 U11 w: 0 s w: 0 #isNat w: 0 U42 w: 0 top w: 0 #plus w: 0 #top w: 0 U12 w: 0 #U42 w: 0 #U12 w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 #s w: x1 mark w: x1 + 1 #proper w: 0 isNat w: 0 plus w: 0 #U11 w: 0 active w: 0 U31 w: 0 #U41 w: 0 #active w: 0 #U21 w: 0 tt w: 0 U41 w: 0 #U31 w: 0 USABLE RULES: { } Removed DPs: #14 #55 Number of SCCs: 8, DPs: 38 SCC { #19 #76 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.