/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: U101(tt(),M,N) -> U102(isNatKind(activate(M)),activate(M),activate(N)) 2: U102(tt(),M,N) -> U103(isNat(activate(N)),activate(M),activate(N)) 3: U103(tt(),M,N) -> U104(isNatKind(activate(N)),activate(M),activate(N)) 4: U104(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N)) 5: U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) 6: U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) 7: U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) 8: U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2)) 9: U15(tt(),V2) -> U16(isNat(activate(V2))) 10: U16(tt()) -> tt() 11: U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1)) 12: U22(tt(),V1) -> U23(isNat(activate(V1))) 13: U23(tt()) -> tt() 14: U31(tt(),V1,V2) -> U32(isNatKind(activate(V1)),activate(V1),activate(V2)) 15: U32(tt(),V1,V2) -> U33(isNatKind(activate(V2)),activate(V1),activate(V2)) 16: U33(tt(),V1,V2) -> U34(isNatKind(activate(V2)),activate(V1),activate(V2)) 17: U34(tt(),V1,V2) -> U35(isNat(activate(V1)),activate(V2)) 18: U35(tt(),V2) -> U36(isNat(activate(V2))) 19: U36(tt()) -> tt() 20: U41(tt(),V2) -> U42(isNatKind(activate(V2))) 21: U42(tt()) -> tt() 22: U51(tt()) -> tt() 23: U61(tt(),V2) -> U62(isNatKind(activate(V2))) 24: U62(tt()) -> tt() 25: U71(tt(),N) -> U72(isNatKind(activate(N)),activate(N)) 26: U72(tt(),N) -> activate(N) 27: U81(tt(),M,N) -> U82(isNatKind(activate(M)),activate(M),activate(N)) 28: U82(tt(),M,N) -> U83(isNat(activate(N)),activate(M),activate(N)) 29: U83(tt(),M,N) -> U84(isNatKind(activate(N)),activate(M),activate(N)) 30: U84(tt(),M,N) -> s(plus(activate(N),activate(M))) 31: U91(tt(),N) -> U92(isNatKind(activate(N))) 32: U92(tt()) -> 0() 33: isNat(n__0()) -> tt() 34: isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) 35: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) 36: isNat(n__x(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V1),activate(V2)) 37: isNatKind(n__0()) -> tt() 38: isNatKind(n__plus(V1,V2)) -> U41(isNatKind(activate(V1)),activate(V2)) 39: isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1))) 40: isNatKind(n__x(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2)) 41: plus(N,0()) -> U71(isNat(N),N) 42: plus(N,s(M)) -> U81(isNat(M),M,N) 43: x(N,0()) -> U91(isNat(N),N) 44: x(N,s(M)) -> U101(isNat(M),M,N) 45: 0() -> n__0() 46: plus(X1,X2) -> n__plus(X1,X2) 47: s(X) -> n__s(X) 48: x(X1,X2) -> n__x(X1,X2) 49: activate(n__0()) -> 0() 50: activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2)) 51: activate(n__s(X)) -> s(activate(X)) 52: activate(n__x(X1,X2)) -> x(activate(X1),activate(X2)) 53: activate(X) -> X Number of strict rules: 53 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #U102(tt(),M,N) -> #U103(isNat(activate(N)),activate(M),activate(N)) #2: #U102(tt(),M,N) -> #isNat(activate(N)) #3: #U102(tt(),M,N) -> #activate(N) #4: #U102(tt(),M,N) -> #activate(M) #5: #U102(tt(),M,N) -> #activate(N) #6: #x(N,0()) -> #U91(isNat(N),N) #7: #x(N,0()) -> #isNat(N) #8: #U83(tt(),M,N) -> #U84(isNatKind(activate(N)),activate(M),activate(N)) #9: #U83(tt(),M,N) -> #isNatKind(activate(N)) #10: #U83(tt(),M,N) -> #activate(N) #11: #U83(tt(),M,N) -> #activate(M) #12: #U83(tt(),M,N) -> #activate(N) #13: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1)) #14: #isNat(n__s(V1)) -> #isNatKind(activate(V1)) #15: #isNat(n__s(V1)) -> #activate(V1) #16: #isNat(n__s(V1)) -> #activate(V1) #17: #plus(N,s(M)) -> #U81(isNat(M),M,N) #18: #plus(N,s(M)) -> #isNat(M) #19: #plus(N,0()) -> #U71(isNat(N),N) #20: #plus(N,0()) -> #isNat(N) #21: #isNatKind(n__plus(V1,V2)) -> #U41(isNatKind(activate(V1)),activate(V2)) #22: #isNatKind(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #23: #isNatKind(n__plus(V1,V2)) -> #activate(V1) #24: #isNatKind(n__plus(V1,V2)) -> #activate(V2) #25: #U12(tt(),V1,V2) -> #U13(isNatKind(activate(V2)),activate(V1),activate(V2)) #26: #U12(tt(),V1,V2) -> #isNatKind(activate(V2)) #27: #U12(tt(),V1,V2) -> #activate(V2) #28: #U12(tt(),V1,V2) -> #activate(V1) #29: #U12(tt(),V1,V2) -> #activate(V2) #30: #isNatKind(n__x(V1,V2)) -> #U61(isNatKind(activate(V1)),activate(V2)) #31: #isNatKind(n__x(V1,V2)) -> #isNatKind(activate(V1)) #32: #isNatKind(n__x(V1,V2)) -> #activate(V1) #33: #isNatKind(n__x(V1,V2)) -> #activate(V2) #34: #activate(n__s(X)) -> #s(activate(X)) #35: #activate(n__s(X)) -> #activate(X) #36: #U15(tt(),V2) -> #U16(isNat(activate(V2))) #37: #U15(tt(),V2) -> #isNat(activate(V2)) #38: #U15(tt(),V2) -> #activate(V2) #39: #U21(tt(),V1) -> #U22(isNatKind(activate(V1)),activate(V1)) #40: #U21(tt(),V1) -> #isNatKind(activate(V1)) #41: #U21(tt(),V1) -> #activate(V1) #42: #U21(tt(),V1) -> #activate(V1) #43: #U61(tt(),V2) -> #U62(isNatKind(activate(V2))) #44: #U61(tt(),V2) -> #isNatKind(activate(V2)) #45: #U61(tt(),V2) -> #activate(V2) #46: #U22(tt(),V1) -> #U23(isNat(activate(V1))) #47: #U22(tt(),V1) -> #isNat(activate(V1)) #48: #U22(tt(),V1) -> #activate(V1) #49: #U91(tt(),N) -> #U92(isNatKind(activate(N))) #50: #U91(tt(),N) -> #isNatKind(activate(N)) #51: #U91(tt(),N) -> #activate(N) #52: #U31(tt(),V1,V2) -> #U32(isNatKind(activate(V1)),activate(V1),activate(V2)) #53: #U31(tt(),V1,V2) -> #isNatKind(activate(V1)) #54: #U31(tt(),V1,V2) -> #activate(V1) #55: #U31(tt(),V1,V2) -> #activate(V1) #56: #U31(tt(),V1,V2) -> #activate(V2) #57: #U84(tt(),M,N) -> #s(plus(activate(N),activate(M))) #58: #U84(tt(),M,N) -> #plus(activate(N),activate(M)) #59: #U84(tt(),M,N) -> #activate(N) #60: #U84(tt(),M,N) -> #activate(M) #61: #activate(n__x(X1,X2)) -> #x(activate(X1),activate(X2)) #62: #activate(n__x(X1,X2)) -> #activate(X1) #63: #activate(n__x(X1,X2)) -> #activate(X2) #64: #activate(n__0()) -> #0() #65: #U71(tt(),N) -> #U72(isNatKind(activate(N)),activate(N)) #66: #U71(tt(),N) -> #isNatKind(activate(N)) #67: #U71(tt(),N) -> #activate(N) #68: #U71(tt(),N) -> #activate(N) #69: #U41(tt(),V2) -> #U42(isNatKind(activate(V2))) #70: #U41(tt(),V2) -> #isNatKind(activate(V2)) #71: #U41(tt(),V2) -> #activate(V2) #72: #U13(tt(),V1,V2) -> #U14(isNatKind(activate(V2)),activate(V1),activate(V2)) #73: #U13(tt(),V1,V2) -> #isNatKind(activate(V2)) #74: #U13(tt(),V1,V2) -> #activate(V2) #75: #U13(tt(),V1,V2) -> #activate(V1) #76: #U13(tt(),V1,V2) -> #activate(V2) #77: #isNatKind(n__s(V1)) -> #U51(isNatKind(activate(V1))) #78: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1)) #79: #isNatKind(n__s(V1)) -> #activate(V1) #80: #U11(tt(),V1,V2) -> #U12(isNatKind(activate(V1)),activate(V1),activate(V2)) #81: #U11(tt(),V1,V2) -> #isNatKind(activate(V1)) #82: #U11(tt(),V1,V2) -> #activate(V1) #83: #U11(tt(),V1,V2) -> #activate(V1) #84: #U11(tt(),V1,V2) -> #activate(V2) #85: #x(N,s(M)) -> #U101(isNat(M),M,N) #86: #x(N,s(M)) -> #isNat(M) #87: #U82(tt(),M,N) -> #U83(isNat(activate(N)),activate(M),activate(N)) #88: #U82(tt(),M,N) -> #isNat(activate(N)) #89: #U82(tt(),M,N) -> #activate(N) #90: #U82(tt(),M,N) -> #activate(M) #91: #U82(tt(),M,N) -> #activate(N) #92: #isNat(n__plus(V1,V2)) -> #U11(isNatKind(activate(V1)),activate(V1),activate(V2)) #93: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #94: #isNat(n__plus(V1,V2)) -> #activate(V1) #95: #isNat(n__plus(V1,V2)) -> #activate(V1) #96: #isNat(n__plus(V1,V2)) -> #activate(V2) #97: #U81(tt(),M,N) -> #U82(isNatKind(activate(M)),activate(M),activate(N)) #98: #U81(tt(),M,N) -> #isNatKind(activate(M)) #99: #U81(tt(),M,N) -> #activate(M) #100: #U81(tt(),M,N) -> #activate(M) #101: #U81(tt(),M,N) -> #activate(N) #102: #U34(tt(),V1,V2) -> #U35(isNat(activate(V1)),activate(V2)) #103: #U34(tt(),V1,V2) -> #isNat(activate(V1)) #104: #U34(tt(),V1,V2) -> #activate(V1) #105: #U34(tt(),V1,V2) -> #activate(V2) #106: #U92(tt()) -> #0() #107: #U72(tt(),N) -> #activate(N) #108: #isNat(n__x(V1,V2)) -> #U31(isNatKind(activate(V1)),activate(V1),activate(V2)) #109: #isNat(n__x(V1,V2)) -> #isNatKind(activate(V1)) #110: #isNat(n__x(V1,V2)) -> #activate(V1) #111: #isNat(n__x(V1,V2)) -> #activate(V1) #112: #isNat(n__x(V1,V2)) -> #activate(V2) #113: #U33(tt(),V1,V2) -> #U34(isNatKind(activate(V2)),activate(V1),activate(V2)) #114: #U33(tt(),V1,V2) -> #isNatKind(activate(V2)) #115: #U33(tt(),V1,V2) -> #activate(V2) #116: #U33(tt(),V1,V2) -> #activate(V1) #117: #U33(tt(),V1,V2) -> #activate(V2) #118: #U103(tt(),M,N) -> #U104(isNatKind(activate(N)),activate(M),activate(N)) #119: #U103(tt(),M,N) -> #isNatKind(activate(N)) #120: #U103(tt(),M,N) -> #activate(N) #121: #U103(tt(),M,N) -> #activate(M) #122: #U103(tt(),M,N) -> #activate(N) #123: #U101(tt(),M,N) -> #U102(isNatKind(activate(M)),activate(M),activate(N)) #124: #U101(tt(),M,N) -> #isNatKind(activate(M)) #125: #U101(tt(),M,N) -> #activate(M) #126: #U101(tt(),M,N) -> #activate(M) #127: #U101(tt(),M,N) -> #activate(N) #128: #U14(tt(),V1,V2) -> #U15(isNat(activate(V1)),activate(V2)) #129: #U14(tt(),V1,V2) -> #isNat(activate(V1)) #130: #U14(tt(),V1,V2) -> #activate(V1) #131: #U14(tt(),V1,V2) -> #activate(V2) #132: #U32(tt(),V1,V2) -> #U33(isNatKind(activate(V2)),activate(V1),activate(V2)) #133: #U32(tt(),V1,V2) -> #isNatKind(activate(V2)) #134: #U32(tt(),V1,V2) -> #activate(V2) #135: #U32(tt(),V1,V2) -> #activate(V1) #136: #U32(tt(),V1,V2) -> #activate(V2) #137: #U104(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N)) #138: #U104(tt(),M,N) -> #x(activate(N),activate(M)) #139: #U104(tt(),M,N) -> #activate(N) #140: #U104(tt(),M,N) -> #activate(M) #141: #U104(tt(),M,N) -> #activate(N) #142: #activate(n__plus(X1,X2)) -> #plus(activate(X1),activate(X2)) #143: #activate(n__plus(X1,X2)) -> #activate(X1) #144: #activate(n__plus(X1,X2)) -> #activate(X2) #145: #U35(tt(),V2) -> #U36(isNat(activate(V2))) #146: #U35(tt(),V2) -> #isNat(activate(V2)) #147: #U35(tt(),V2) -> #activate(V2) Number of SCCs: 1, DPs: 136 SCC { #1..33 #35 #37..42 #44 #45 #47 #48 #50..56 #58..63 #65..68 #70..76 #78..105 #107..144 #146 #147 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 #U72 w: max(x2) #U32 w: max(x2, x3) isNatKind w: x1 U16 w: 0 U21 w: 0 #U83 w: max(x2 + 2, x3) U11 w: 0 s w: x1 #isNat w: x1 U42 w: 1 U91 w: max(x1 + 1) #U35 w: max(x2) #U101 w: max(x2, x3 + 2) activate w: x1 #U82 w: max(x2 + 2, x3) #U104 w: max(x2, x3 + 2) U71 w: max(x2) #U81 w: max(x1 + 1, x2 + 2, x3) #U92 w: 0 #plus w: max(x1, x2 + 2) U101 w: max(x2, x3 + 2) #activate w: x1 U103 w: max(x2, x3 + 2) #U23 w: 0 U84 w: max(x2 + 2, x3) U23 w: 0 U35 w: 0 U72 w: max(x2) #U13 w: max(x2, x3) U34 w: 0 #U103 w: max(x2, x3 + 2) U12 w: 0 #U33 w: max(x2, x3) x w: max(x1 + 2, x2) #U16 w: 0 n__s w: x1 U104 w: max(x2, x3 + 2) #U42 w: 0 #U12 w: max(x2, x3) #U62 w: 0 U83 w: max(x2 + 2, x3) 0 w: 0 #U14 w: max(x2, x3) #U36 w: 0 U36 w: 0 #U102 w: max(x2, x3 + 2) #x w: max(x1 + 2, x2) #s w: 0 U62 w: 1 n__plus w: max(x1, x2 + 2) #U15 w: max(x2) U32 w: 0 U33 w: 0 n__0 w: 0 #U34 w: max(x2, x3) U14 w: 0 isNat w: x1 n__x w: max(x1 + 2, x2) plus w: max(x1, x2 + 2) U15 w: 0 U61 w: 0 #U51 w: 0 #U11 w: max(x2, x3) U31 w: max(x2 + 1) U92 w: 1 #U41 w: max(x2) U102 w: max(x2, x3 + 2) #U21 w: max(x2) U81 w: max(x1 + 2, x2 + 2, x3) U82 w: max(x2 + 2, x3) #U22 w: max(x2) tt w: 0 #U84 w: max(x2 + 2, x3) #U71 w: max(x2) U13 w: 0 U22 w: 0 U51 w: 0 #isNatKind w: x1 U41 w: 0 #U31 w: max(x2, x3) #U91 w: max(x1 + 2, x2) #U61 w: max(x2) USABLE RULES: { 1..19 21 22 24..37 39 41..53 } Removed DPs: #2 #3 #5 #7 #11 #18 #21 #24 #31 #32 #60 #62 #90 #96 #98..100 #109..111 #119 #120 #122 #127 #139 #141 #144 Number of SCCs: 1, DPs: 107 SCC { #1 #4 #6 #8..10 #12..17 #19 #20 #22 #23 #25..30 #33 #35 #37..42 #44 #45 #47 #48 #50..56 #58 #59 #61 #63 #65..68 #72..76 #78..89 #91..95 #97 #101..105 #107 #108 #112..118 #121 #123..126 #128..138 #140 #142 #143 #146 #147 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 #U72 w: max(x2 + 3) #U32 w: max(x2 + 4, x3 + 3) isNatKind w: x1 U16 w: 0 U21 w: 0 #U83 w: max(x2 + 2, x3 + 3) U11 w: 0 s w: x1 #isNat w: x1 + 3 U42 w: 1 U91 w: max(x1 + 1) #U35 w: max(x2 + 3) #U101 w: max(x2 + 3, x3 + 6) activate w: x1 #U82 w: max(x2 + 2, x3 + 3) #U104 w: max(x2 + 3, x3 + 6) U71 w: max(x2) #U81 w: max(x1 + 1, x2 + 2, x3 + 3) #U92 w: 0 #plus w: max(x1 + 3, x2 + 2) U101 w: max(x2, x3 + 3) #activate w: x1 + 3 U103 w: max(x2, x3 + 3) #U23 w: 0 U84 w: max(x2 + 3, x3) U23 w: 0 U35 w: 0 U72 w: max(x2) #U13 w: max(x2 + 3, x3 + 5) U34 w: 0 #U103 w: max(x2 + 3, x3 + 6) U12 w: 0 #U33 w: max(x2 + 4, x3 + 3) x w: max(x1 + 3, x2) #U16 w: 0 n__s w: x1 U104 w: max(x2, x3 + 3) #U42 w: 0 #U12 w: max(x2 + 3, x3 + 6) #U62 w: 0 U83 w: max(x2 + 3, x3) 0 w: 0 #U14 w: max(x2 + 3, x3 + 5) #U36 w: 0 U36 w: 0 #U102 w: max(x2 + 3, x3 + 6) #x w: max(x1 + 6, x2 + 3) #s w: 0 U62 w: 1 n__plus w: max(x1, x2 + 3) #U15 w: max(x2 + 4) U32 w: 0 U33 w: 0 n__0 w: 0 #U34 w: max(x2 + 4, x3 + 3) U14 w: 0 isNat w: x1 n__x w: max(x1 + 3, x2) plus w: max(x1, x2 + 3) U15 w: 0 U61 w: 0 #U51 w: 0 #U11 w: max(x2 + 3, x3 + 6) U31 w: max(x2 + 1) U92 w: 1 #U41 w: max(x2) U102 w: max(x2, x3 + 3) #U21 w: max(x2 + 3) U81 w: max(x1 + 3, x2 + 3, x3) U82 w: max(x2 + 3, x3) #U22 w: max(x2 + 3) tt w: 0 #U84 w: max(x2 + 2, x3 + 3) #U71 w: max(x2 + 3) U13 w: 0 U22 w: 0 U51 w: 0 #isNatKind w: x1 + 3 U41 w: 0 #U31 w: max(x2 + 6, x3 + 3) #U91 w: max(x1 + 2, x2 + 4) #U61 w: max(x2 + 3) USABLE RULES: { 1..19 21 22 24..37 39 41..53 } Removed DPs: #6 #26 #27 #29 #37 #38 #50 #51 #53..55 #73 #74 #76 #84 #103 #104 #116 #128 #131 #135 Number of SCCs: 1, DPs: 86 SCC { #1 #4 #8..10 #12..17 #19 #20 #22 #23 #25 #28 #30 #33 #35 #39..42 #44 #45 #47 #48 #52 #56 #58 #59 #61 #63 #65..68 #72 #75 #78..83 #85..89 #91..95 #97 #101 #102 #105 #107 #108 #112..115 #117 #118 #121 #123..126 #129 #130 #132..134 #136..138 #140 #142 #143 #146 #147 } POLO(Sum)... succeeded. #0 w: 0 #U72 w: x1 + x2 + 1 #U32 w: x1 + x3 + 5 isNatKind w: 6 U16 w: 0 U21 w: x2 + 2 #U83 w: x3 + 7 U11 w: 0 s w: x1 #isNat w: x1 + 7 U42 w: 6 U91 w: 3 #U35 w: x2 + 8 #U101 w: x2 + x3 + 13 activate w: x1 #U82 w: x1 + x3 + 1 #U104 w: x1 + x2 + x3 + 7 U71 w: x2 #U81 w: x3 + 7 #U92 w: 0 #plus w: x1 + 7 U101 w: x2 + x3 + 6 #activate w: x1 + 7 U103 w: x2 + x3 + 6 #U23 w: 0 U84 w: x3 U23 w: x1 + 1 U35 w: 4 U72 w: x2 #U13 w: x2 + 7 U34 w: x3 + 3 #U103 w: x2 + x3 + 13 U12 w: x1 + x2 + x3 #U33 w: x3 + 10 x w: x1 + x2 + 6 #U16 w: 0 n__s w: x1 U104 w: x2 + x3 + 6 #U42 w: 0 #U12 w: x1 + x2 + 1 #U62 w: 0 U83 w: x3 0 w: 1 #U14 w: x2 + 7 #U36 w: 0 U36 w: 5 #U102 w: x1 + x2 + x3 + 7 #x w: x1 + x2 + 13 #s w: 0 U62 w: 6 n__plus w: x1 #U15 w: 4 U32 w: 1 U33 w: x2 + 2 n__0 w: 1 #U34 w: x1 + x3 + 3 U14 w: x1 isNat w: x1 + 1 n__x w: x1 + x2 + 6 plus w: x1 U15 w: x1 + 6 U61 w: 6 #U51 w: 0 #U11 w: x2 + 7 U31 w: 0 U92 w: 1 #U41 w: 4 U102 w: x1 + x2 + x3 #U21 w: x2 + 7 U81 w: x3 U82 w: x3 #U22 w: x2 + 7 tt w: 6 #U84 w: x1 + x3 + 1 #U71 w: x2 + 7 U13 w: 5 U22 w: x2 + 3 U51 w: x1 #isNatKind w: x1 + 7 U41 w: x1 #U31 w: x3 + 12 #U91 w: 4 #U61 w: x2 + 8 USABLE RULES: { 1..4 20..32 37..53 } Removed DPs: #4 #30 #33 #44 #45 #52 #56 #63 #86 #102 #105 #108 #112..115 #117 #121 #124..126 #132..134 #136 #140 #146 #147 Number of SCCs: 1, DPs: 58 SCC { #1 #8..10 #12..17 #19 #20 #22 #23 #25 #28 #35 #39..42 #47 #48 #58 #59 #61 #65..68 #72 #75 #78..83 #85 #87..89 #91..95 #97 #101 #107 #118 #123 #129 #130 #137 #138 #142 #143 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #0 s: [] p: 0 #U72 s: 2 #U32 s: [] p: 0 isNatKind s: [] p: 6 U16 s: [] p: 6 U21 s: [] p: 6 #U83 s: 3 U11 s: 1 s s: [1] p: 6 #isNat s: 1 U42 s: [] p: 6 U91 s: 1 #U35 s: [1,2] p: 0 #U101 s: [2,3,1] p: 9 activate s: 1 #U82 s: 3 #U104 s: [2,3] p: 9 U71 s: 2 #U81 s: 3 #U92 s: [] p: 0 #plus s: 1 U101 s: [2,3,1] p: 9 #activate s: 1 U103 s: [2,3,1] p: 9 #U23 s: [] p: 0 U84 s: [3,2,1] p: 7 U23 s: [] p: 6 U35 s: 1 U72 s: 2 #U13 s: 2 U34 s: 1 #U103 s: [2,3,1] p: 9 U12 s: 1 #U33 s: [3] p: 0 x s: [2,1] p: 9 #U16 s: [] p: 0 n__s s: [1] p: 6 U104 s: [2,3,1] p: 9 #U42 s: [] p: 0 #U12 s: [2] p: 2 #U62 s: [] p: 0 U83 s: [3,2,1] p: 7 0 s: [] p: 5 #U14 s: 2 #U36 s: [] p: 0 U36 s: [] p: 6 #U102 s: [2,3,1] p: 9 #x s: [2,1] p: 9 #s s: [] p: 0 U62 s: [] p: 6 n__plus s: [1,2] p: 7 #U15 s: [2,1] p: 0 U32 s: [] p: 6 U33 s: 1 n__0 s: [] p: 5 #U34 s: [2,3] p: 0 U14 s: 1 isNat s: [] p: 6 n__x s: [2,1] p: 9 plus s: [1,2] p: 7 U15 s: 1 U61 s: [] p: 6 #U51 s: [] p: 0 #U11 s: [2,3] p: 7 U31 s: 1 U92 s: 1 #U41 s: [] p: 0 U102 s: [2,3,1] p: 9 #U21 s: [2] p: 6 U81 s: [3,2,1] p: 7 U82 s: [3,2,1] p: 7 #U22 s: [1,2] p: 2 tt s: [] p: 6 #U84 s: 3 #U71 s: 2 U13 s: 1 U22 s: [] p: 6 U51 s: [] p: 6 #isNatKind s: 1 U41 s: 1 #U31 s: [1,3] p: 0 #U91 s: [2,1] p: 0 #U61 s: [2,1] p: 0 USABLE RULES: { 1..53 } Removed DPs: #14..16 #22 #23 #25 #28 #35 #39..42 #47 #48 #78..83 #85 #93..95 #118 #142 #143 Number of SCCs: 1, DPs: 5 SCC { #8 #17 #58 #87 #97 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #0 s: [] p: 0 #U72 s: [] p: 3 #U32 s: [] p: 0 isNatKind s: [] p: 4 U16 s: 1 U21 s: 1 #U83 s: [2] p: 1 U11 s: [] p: 4 s s: [1] p: 4 #isNat s: [] p: 2 U42 s: [] p: 4 U91 s: [1] p: 5 #U35 s: [1,2] p: 0 #U101 s: [] p: 9 activate s: 1 #U82 s: [2] p: 3 #U104 s: [] p: 9 U71 s: [2,1] p: 1 #U81 s: [2] p: 4 #U92 s: [] p: 0 #plus s: 2 U101 s: [3,2,1] p: 6 #activate s: [] p: 2 U103 s: [3,2,1] p: 6 #U23 s: [] p: 0 U84 s: [3,2,1] p: 5 U23 s: [] p: 4 U35 s: [] p: 4 U72 s: 2 #U13 s: [3,1] p: 7 U34 s: [] p: 4 #U103 s: [] p: 9 U12 s: 1 #U33 s: [3] p: 0 x s: [1,2] p: 6 #U16 s: [] p: 0 n__s s: [1] p: 4 U104 s: [3,2,1] p: 6 #U42 s: [] p: 0 #U12 s: [3] p: 2 #U62 s: [] p: 0 U83 s: [3,2,1] p: 5 0 s: [] p: 0 #U14 s: [3,2] p: 3 #U36 s: [] p: 0 U36 s: [] p: 4 #U102 s: [] p: 9 #x s: [] p: 9 #s s: [] p: 0 U62 s: [] p: 4 n__plus s: [1,2] p: 5 #U15 s: [2,1] p: 0 U32 s: 1 U33 s: 1 n__0 s: [] p: 0 #U34 s: [3] p: 0 U14 s: [] p: 4 isNat s: [] p: 4 n__x s: [1,2] p: 6 plus s: [1,2] p: 5 U15 s: [] p: 4 U61 s: 1 #U51 s: [] p: 0 #U11 s: [] p: 7 U31 s: 1 U92 s: [] p: 3 #U41 s: [] p: 0 U102 s: [3,2,1] p: 6 #U21 s: [] p: 6 U81 s: [3,2,1] p: 5 U82 s: [3,2,1] p: 5 #U22 s: [1] p: 2 tt s: [] p: 4 #U84 s: 2 #U71 s: 2 U13 s: [] p: 4 U22 s: [] p: 4 U51 s: [] p: 4 #isNatKind s: [] p: 2 U41 s: 1 #U31 s: [1,3] p: 0 #U91 s: [2,1] p: 0 #U61 s: [2,1] p: 0 USABLE RULES: { 1..53 } Removed DPs: #8 #87 #97 Number of SCCs: 0, DPs: 0