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(X1,X2) 51: activate(n__s(X)) -> s(X) 52: activate(n__x(X1,X2)) -> x(X1,X2) 53: activate(X) -> X Number of strict rules: 53 Direct Order(PosReal,>,Poly) ... failed. Freezing ... 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(X) #35: #U15(tt(),V2) -> #U16(isNat(activate(V2))) #36: #U15(tt(),V2) -> #isNat(activate(V2)) #37: #U15(tt(),V2) -> #activate(V2) #38: #U21(tt(),V1) -> #U22(isNatKind(activate(V1)),activate(V1)) #39: #U21(tt(),V1) -> #isNatKind(activate(V1)) #40: #U21(tt(),V1) -> #activate(V1) #41: #U21(tt(),V1) -> #activate(V1) #42: #U61(tt(),V2) -> #U62(isNatKind(activate(V2))) #43: #U61(tt(),V2) -> #isNatKind(activate(V2)) #44: #U61(tt(),V2) -> #activate(V2) #45: #U22(tt(),V1) -> #U23(isNat(activate(V1))) #46: #U22(tt(),V1) -> #isNat(activate(V1)) #47: #U22(tt(),V1) -> #activate(V1) #48: #U91(tt(),N) -> #U92(isNatKind(activate(N))) #49: #U91(tt(),N) -> #isNatKind(activate(N)) #50: #U91(tt(),N) -> #activate(N) #51: #U31(tt(),V1,V2) -> #U32(isNatKind(activate(V1)),activate(V1),activate(V2)) #52: #U31(tt(),V1,V2) -> #isNatKind(activate(V1)) #53: #U31(tt(),V1,V2) -> #activate(V1) #54: #U31(tt(),V1,V2) -> #activate(V1) #55: #U31(tt(),V1,V2) -> #activate(V2) #56: #U84(tt(),M,N) -> #s(plus(activate(N),activate(M))) #57: #U84(tt(),M,N) -> #plus(activate(N),activate(M)) #58: #U84(tt(),M,N) -> #activate(N) #59: #U84(tt(),M,N) -> #activate(M) #60: #activate(n__x(X1,X2)) -> #x(X1,X2) #61: #activate(n__0()) -> #0() #62: #U71(tt(),N) -> #U72(isNatKind(activate(N)),activate(N)) #63: #U71(tt(),N) -> #isNatKind(activate(N)) #64: #U71(tt(),N) -> #activate(N) #65: #U71(tt(),N) -> #activate(N) #66: #U41(tt(),V2) -> #U42(isNatKind(activate(V2))) #67: #U41(tt(),V2) -> #isNatKind(activate(V2)) #68: #U41(tt(),V2) -> #activate(V2) #69: #U13(tt(),V1,V2) -> #U14(isNatKind(activate(V2)),activate(V1),activate(V2)) #70: #U13(tt(),V1,V2) -> #isNatKind(activate(V2)) #71: #U13(tt(),V1,V2) -> #activate(V2) #72: #U13(tt(),V1,V2) -> #activate(V1) #73: #U13(tt(),V1,V2) -> #activate(V2) #74: #isNatKind(n__s(V1)) -> #U51(isNatKind(activate(V1))) #75: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1)) #76: #isNatKind(n__s(V1)) -> #activate(V1) #77: #U11(tt(),V1,V2) -> #U12(isNatKind(activate(V1)),activate(V1),activate(V2)) #78: #U11(tt(),V1,V2) -> #isNatKind(activate(V1)) #79: #U11(tt(),V1,V2) -> #activate(V1) #80: #U11(tt(),V1,V2) -> #activate(V1) #81: #U11(tt(),V1,V2) -> #activate(V2) #82: #x(N,s(M)) -> #U101(isNat(M),M,N) #83: #x(N,s(M)) -> #isNat(M) #84: #U82(tt(),M,N) -> #U83(isNat(activate(N)),activate(M),activate(N)) #85: #U82(tt(),M,N) -> #isNat(activate(N)) #86: #U82(tt(),M,N) -> #activate(N) #87: #U82(tt(),M,N) -> #activate(M) #88: #U82(tt(),M,N) -> #activate(N) #89: #isNat(n__plus(V1,V2)) -> #U11(isNatKind(activate(V1)),activate(V1),activate(V2)) #90: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1)) #91: #isNat(n__plus(V1,V2)) -> #activate(V1) #92: #isNat(n__plus(V1,V2)) -> #activate(V1) #93: #isNat(n__plus(V1,V2)) -> #activate(V2) #94: #U81(tt(),M,N) -> #U82(isNatKind(activate(M)),activate(M),activate(N)) #95: #U81(tt(),M,N) -> #isNatKind(activate(M)) #96: #U81(tt(),M,N) -> #activate(M) #97: #U81(tt(),M,N) -> #activate(M) #98: #U81(tt(),M,N) -> #activate(N) #99: #U34(tt(),V1,V2) -> #U35(isNat(activate(V1)),activate(V2)) #100: #U34(tt(),V1,V2) -> #isNat(activate(V1)) #101: #U34(tt(),V1,V2) -> #activate(V1) #102: #U34(tt(),V1,V2) -> #activate(V2) #103: #U92(tt()) -> #0() #104: #U72(tt(),N) -> #activate(N) #105: #isNat(n__x(V1,V2)) -> #U31(isNatKind(activate(V1)),activate(V1),activate(V2)) #106: #isNat(n__x(V1,V2)) -> #isNatKind(activate(V1)) #107: #isNat(n__x(V1,V2)) -> #activate(V1) #108: #isNat(n__x(V1,V2)) -> #activate(V1) #109: #isNat(n__x(V1,V2)) -> #activate(V2) #110: #U33(tt(),V1,V2) -> #U34(isNatKind(activate(V2)),activate(V1),activate(V2)) #111: #U33(tt(),V1,V2) -> #isNatKind(activate(V2)) #112: #U33(tt(),V1,V2) -> #activate(V2) #113: #U33(tt(),V1,V2) -> #activate(V1) #114: #U33(tt(),V1,V2) -> #activate(V2) #115: #U103(tt(),M,N) -> #U104(isNatKind(activate(N)),activate(M),activate(N)) #116: #U103(tt(),M,N) -> #isNatKind(activate(N)) #117: #U103(tt(),M,N) -> #activate(N) #118: #U103(tt(),M,N) -> #activate(M) #119: #U103(tt(),M,N) -> #activate(N) #120: #U101(tt(),M,N) -> #U102(isNatKind(activate(M)),activate(M),activate(N)) #121: #U101(tt(),M,N) -> #isNatKind(activate(M)) #122: #U101(tt(),M,N) -> #activate(M) #123: #U101(tt(),M,N) -> #activate(M) #124: #U101(tt(),M,N) -> #activate(N) #125: #U14(tt(),V1,V2) -> #U15(isNat(activate(V1)),activate(V2)) #126: #U14(tt(),V1,V2) -> #isNat(activate(V1)) #127: #U14(tt(),V1,V2) -> #activate(V1) #128: #U14(tt(),V1,V2) -> #activate(V2) #129: #U32(tt(),V1,V2) -> #U33(isNatKind(activate(V2)),activate(V1),activate(V2)) #130: #U32(tt(),V1,V2) -> #isNatKind(activate(V2)) #131: #U32(tt(),V1,V2) -> #activate(V2) #132: #U32(tt(),V1,V2) -> #activate(V1) #133: #U32(tt(),V1,V2) -> #activate(V2) #134: #U104(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N)) #135: #U104(tt(),M,N) -> #x(activate(N),activate(M)) #136: #U104(tt(),M,N) -> #activate(N) #137: #U104(tt(),M,N) -> #activate(M) #138: #U104(tt(),M,N) -> #activate(N) #139: #activate(n__plus(X1,X2)) -> #plus(X1,X2) #140: #U35(tt(),V2) -> #U36(isNat(activate(V2))) #141: #U35(tt(),V2) -> #isNat(activate(V2)) #142: #U35(tt(),V2) -> #activate(V2) Number of SCCs: 1, DPs: 131, edges: 619 SCC { #1..33 #36..41 #43 #44 #46 #47 #49..55 #57..60 #62..65 #67..73 #75..102 #104..139 #141 #142 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded. #0() weight: 0 #U72(x1,x2) weight: max{0, x2} #U32(x1,x2,x3) weight: max{(/ 1 4) + x3, (/ 1 8) + x2, (/ 1 8) + x1} isNatKind(x1) weight: (/ 1 8) U16(x1) weight: (/ 1 8) U21(x1,x2) weight: max{0, x2} #U83(x1,x2,x3) weight: max{0, x3, (/ 5 8) + x2} U11(x1,x2,x3) weight: max{0, (/ 1 4) + x3} s(x1) weight: x1 #isNat(x1) weight: x1 U42(x1) weight: (/ 1 8) U91(x1,x2) weight: max{0, (/ 1 8) + x2} #U35(x1,x2) weight: max{0, x2} #U101(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 1 2) + x2} activate(x1) weight: x1 #U82(x1,x2,x3) weight: max{0, x3, (/ 5 8) + x2} #U104(x1,x2,x3) weight: max{(/ 5 8) + x3, (/ 1 2) + x2, x1} U71(x1,x2) weight: max{0, x2} #U81(x1,x2,x3) weight: max{0, x3, (/ 5 8) + x2} #U92(x1) weight: 0 #plus(x1,x2) weight: max{(/ 5 8) + x2, x1} U101(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 1 2) + x2} #activate(x1) weight: x1 U103(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 1 2) + x2} #U23(x1) weight: 0 U84(x1,x2,x3) weight: max{x3, (/ 5 8) + x2, x1} U23(x1) weight: x1 U35(x1,x2) weight: max{0, x1} U72(x1,x2) weight: max{0, x2} #U13(x1,x2,x3) weight: max{x3, x2, (/ 1 2) + x1} U34(x1,x2,x3) weight: max{0, x2, x1} #U103(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 1 2) + x2} U12(x1,x2,x3) weight: max{0, (/ 1 4) + x3} #U33(x1,x2,x3) weight: max{x3, (/ 1 8) + x2, (/ 1 8) + x1} x(x1,x2) weight: max{(/ 1 2) + x2, (/ 5 8) + x1} #U16(x1) weight: 0 n__s(x1) weight: x1 U104(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 1 2) + x2} #U42(x1) weight: 0 #U12(x1,x2,x3) weight: max{(/ 1 2) + x3, x2, (/ 1 2) + x1} #U62(x1) weight: 0 U83(x1,x2,x3) weight: max{x3, (/ 5 8) + x2, x1} 0() weight: (/ 1 8) #U14(x1,x2,x3) weight: max{x3, x2, (/ 1 2) + x1} #U36(x1) weight: 0 U36(x1) weight: (/ 1 8) #U102(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 1 2) + x2} #x(x1,x2) weight: max{(/ 1 2) + x2, (/ 5 8) + x1} #s(x1) weight: 0 U62(x1) weight: (/ 1 8) n__plus(x1,x2) weight: max{(/ 5 8) + x2, x1} #U15(x1,x2) weight: max{0, x2} U32(x1,x2,x3) weight: max{0, (/ 1 8) + x3, (/ 1 4) + x2} U33(x1,x2,x3) weight: max{0, (/ 1 8) + x3, (/ 1 8) + x2} n__0() weight: (/ 1 8) #U34(x1,x2,x3) weight: max{0, x3, (/ 1 8) + x2} U14(x1,x2,x3) weight: max{0, (/ 1 4) + x3} isNat(x1) weight: x1 n__x(x1,x2) weight: max{(/ 1 2) + x2, (/ 5 8) + x1} plus(x1,x2) weight: max{(/ 5 8) + x2, x1} U15(x1,x2) weight: max{0, (/ 1 8) + x2} U61(x1,x2) weight: max{0, x1} #U51(x1) weight: 0 #U11(x1,x2,x3) weight: max{0, (/ 5 8) + x3, x2} U31(x1,x2,x3) weight: max{(/ 1 8) + x3, (/ 5 8) + x2, x1} U92(x1) weight: x1 #U41(x1,x2) weight: max{(/ 1 2) + x2, x1} U102(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 1 2) + x2} #U21(x1,x2) weight: max{0, x2} U81(x1,x2,x3) weight: max{0, x3, (/ 5 8) + x2} U82(x1,x2,x3) weight: max{x3, (/ 5 8) + x2, x1} #U22(x1,x2) weight: max{0, x2} tt() weight: (/ 1 8) #U84(x1,x2,x3) weight: max{0, x3, (/ 5 8) + x2} #U71(x1,x2) weight: max{0, x2} U13(x1,x2,x3) weight: max{0, (/ 1 4) + x3, x1} U22(x1,x2) weight: max{0, x2} U51(x1) weight: (/ 1 8) #isNatKind(x1) weight: x1 U41(x1,x2) weight: max{0, x1} #U31(x1,x2,x3) weight: max{0, (/ 3 8) + x3, (/ 3 8) + x2} #U91(x1,x2) weight: max{0, (/ 1 8) + x2} #U61(x1,x2) weight: max{0, (/ 3 8) + x2} Usable rules: { 1..53 } Removed DPs: #2..7 #11 #18 #21 #24 #26 #27 #29..33 #43 #44 #49..55 #59 #67 #68 #81 #83 #87 #93 #95..97 #100 #101 #105..109 #113 #116..119 #121..124 #130..133 #136..138 Number of SCCs: 1, DPs: 63, edges: 186 SCC { #1 #8..10 #12..17 #19 #20 #22 #23 #25 #28 #36..41 #46 #47 #57 #58 #60 #62..65 #69..73 #75..80 #82 #84..86 #88..92 #94 #98 #104 #115 #120 #125..128 #134 #135 #139 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded. #0() weight: 0 #U72(x1,x2) weight: max{0, (/ 1 4) + x2} #U32(x1,x2,x3) weight: 0 isNatKind(x1) weight: (/ 3 16) U16(x1) weight: 0 U21(x1,x2) weight: max{0, x1} #U83(x1,x2,x3) weight: max{0, (/ 1 4) + x3, (/ 3 4) + x2} U11(x1,x2,x3) weight: max{0, (/ 1 8) + x3, x2} s(x1) weight: x1 #isNat(x1) weight: (/ 1 4) + x1 U42(x1) weight: (/ 1 8) U91(x1,x2) weight: max{0, (/ 3 16) + x2} #U35(x1,x2) weight: 0 #U101(x1,x2,x3) weight: max{0, (/ 3 4) + x3, (/ 13 16) + x2} activate(x1) weight: x1 #U82(x1,x2,x3) weight: max{(/ 1 4) + x3, (/ 3 4) + x2, (/ 9 16) + x1} #U104(x1,x2,x3) weight: max{0, (/ 3 4) + x3, (/ 13 16) + x2} U71(x1,x2) weight: max{0, x2} #U81(x1,x2,x3) weight: max{0, (/ 1 4) + x3, (/ 3 4) + x2} #U92(x1) weight: 0 #plus(x1,x2) weight: max{(/ 3 4) + x2, (/ 1 4) + x1} U101(x1,x2,x3) weight: max{0, (/ 1 2) + x3, (/ 9 16) + x2} #activate(x1) weight: (/ 1 4) + x1 U103(x1,x2,x3) weight: max{0, (/ 1 2) + x3, (/ 9 16) + x2} #U23(x1) weight: 0 U84(x1,x2,x3) weight: max{x3, (/ 1 2) + x2, x1} U23(x1) weight: (/ 1 8) + x1 U35(x1,x2) weight: max{0, (/ 3 8) + x2} U72(x1,x2) weight: max{0, x2} #U13(x1,x2,x3) weight: max{(/ 3 8) + x3, (/ 1 4) + x2, (/ 5 16) + x1} U34(x1,x2,x3) weight: max{0, (/ 5 16) + x3, (/ 5 16) + x2} #U103(x1,x2,x3) weight: max{0, (/ 3 4) + x3, (/ 13 16) + x2} U12(x1,x2,x3) weight: 0 #U33(x1,x2,x3) weight: 0 x(x1,x2) weight: max{(/ 9 16) + x2, (/ 1 2) + x1} #U16(x1) weight: 0 n__s(x1) weight: x1 U104(x1,x2,x3) weight: max{0, (/ 1 2) + x3, (/ 9 16) + x2} #U42(x1) weight: 0 #U12(x1,x2,x3) weight: max{(/ 3 8) + x3, (/ 1 4) + x2, (/ 7 16) + x1} #U62(x1) weight: 0 U83(x1,x2,x3) weight: max{0, x3, (/ 1 2) + x2} 0() weight: (/ 1 16) #U14(x1,x2,x3) weight: max{(/ 3 8) + x3, (/ 1 4) + x2, x1} #U36(x1) weight: 0 U36(x1) weight: 0 #U102(x1,x2,x3) weight: max{0, (/ 3 4) + x3, (/ 13 16) + x2} #x(x1,x2) weight: max{(/ 13 16) + x2, (/ 3 4) + x1} #s(x1) weight: 0 U62(x1) weight: (/ 1 8) n__plus(x1,x2) weight: max{(/ 1 2) + x2, x1} #U15(x1,x2) weight: max{0, (/ 5 16) + x2} U32(x1,x2,x3) weight: max{0, (/ 3 16) + x3} U33(x1,x2,x3) weight: max{0, (/ 1 4) + x3} n__0() weight: (/ 1 16) #U34(x1,x2,x3) weight: 0 U14(x1,x2,x3) weight: max{0, (/ 3 16) + x3} isNat(x1) weight: (/ 1 16) n__x(x1,x2) weight: max{(/ 9 16) + x2, (/ 1 2) + x1} plus(x1,x2) weight: max{(/ 1 2) + x2, x1} U15(x1,x2) weight: max{0, (/ 3 16) + x1} U61(x1,x2) weight: max{0, x1} #U51(x1) weight: 0 #U11(x1,x2,x3) weight: max{0, (/ 11 16) + x3, (/ 1 4) + x2} U31(x1,x2,x3) weight: max{(/ 1 8) + x3, (/ 3 16) + x2, x1} U92(x1) weight: x1 #U41(x1,x2) weight: 0 U102(x1,x2,x3) weight: max{0, (/ 1 2) + x3, (/ 9 16) + x2} #U21(x1,x2) weight: max{(/ 1 4) + x2, x1} U81(x1,x2,x3) weight: max{0, x3, (/ 1 2) + x2} U82(x1,x2,x3) weight: max{0, x3, (/ 1 2) + x2} #U22(x1,x2) weight: max{(/ 1 4) + x2, (/ 1 16) + x1} tt() weight: (/ 1 8) #U84(x1,x2,x3) weight: max{(/ 1 4) + x3, (/ 3 4) + x2, (/ 9 16) + x1} #U71(x1,x2) weight: max{0, (/ 1 4) + x2} U13(x1,x2,x3) weight: max{0, (/ 1 16) + x3, x1} U22(x1,x2) weight: max{x2, x1} U51(x1) weight: (/ 1 8) #isNatKind(x1) weight: (/ 1 4) + x1 U41(x1,x2) weight: max{0, x1} #U31(x1,x2,x3) weight: 0 #U91(x1,x2) weight: 0 #U61(x1,x2) weight: 0 Usable rules: { 1..4 20..32 37..53 } Removed DPs: #36 #37 #70 #71 #73 #125 #128 Number of SCCs: 1, DPs: 56, edges: 159 SCC { #1 #8..10 #12..17 #19 #20 #22 #23 #25 #28 #38..41 #46 #47 #57 #58 #60 #62..65 #69 #72 #75..80 #82 #84..86 #88..92 #94 #98 #104 #115 #120 #126 #127 #134 #135 #139 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded. #0() status: [] precedence above: #U72(x1,x2) status: [x2,x1] precedence above: #U83 #isNat #U82 #U81 #plus #activate #U84 #U71 #isNatKind #U32(x1,x2,x3) status: [x2,x3,x1] precedence above: isNatKind(x1) status: [] precedence above: #U72 U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 U12 n__s U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U16(x1) status: [] precedence above: #U72 isNatKind U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 U12 n__s U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U21(x1,x2) status: [] precedence above: #U72 isNatKind U16 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 U12 n__s U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U83(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 #isNat #U82 #U81 #plus #activate #U84 #U71 #isNatKind U11(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U21 #U83 s #isNat #U82 #U81 #plus #activate U23 U12 n__s U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 s(x1) status: [x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 #isNat #U82 #U81 #plus #activate U23 U12 n__s U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #isNat(x1) status: [x1] precedence above: #isNatKind U42(x1) status: x1 U91(x1,x2) status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 U71 #U81 #plus #activate U23 U12 n__s 0 U32 n__0 U14 isNat U15 U92 #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U35(x1,x2) status: [x2] precedence above: #U101(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 activate #U82 #U104 U71 #U81 #plus U101 #activate U103 U84 U23 #U13 #U103 U12 x n__s U104 #U12 U83 0 #U14 #U102 #x n__plus U32 n__0 U14 isNat n__x plus U15 #U11 U31 U92 U102 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 activate(x1) status: x1 #U82(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 #U83 #isNat #U81 #plus #activate #U84 #U71 #isNatKind #U104(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 #U101 activate #U82 U71 #U81 #plus U101 #activate U103 U84 U23 #U13 #U103 U12 x n__s U104 #U12 U83 0 #U14 #U102 #x n__plus U32 n__0 U14 isNat n__x plus U15 #U11 U31 U92 U102 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U71(x1,x2) status: x2 #U81(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 #U83 #isNat #U82 #plus #activate #U84 #U71 #isNatKind #U92(x1) status: [] precedence above: #plus(x1,x2) status: [x1,x2] precedence above: #U72 #U83 #isNat #U82 #U81 #activate #U84 #U71 #isNatKind U101(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 #U101 activate #U82 #U104 U71 #U81 #plus #activate U103 U84 U23 #U13 #U103 U12 x n__s U104 #U12 U83 0 #U14 #U102 #x n__plus U32 n__0 U14 isNat n__x plus U15 #U11 U31 U92 U102 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #activate(x1) status: [x1] precedence above: #U72 #U83 #isNat #U82 #U81 #plus #U84 #U71 #isNatKind U103(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 #U101 activate #U82 #U104 U71 #U81 #plus U101 #activate U84 U23 #U13 #U103 U12 x n__s U104 #U12 U83 0 #U14 #U102 #x n__plus U32 n__0 U14 isNat n__x plus U15 #U11 U31 U92 U102 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U23(x1) status: [] precedence above: U84(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 #U13 U12 n__s #U12 U83 #U14 n__plus U32 U14 isNat plus #U11 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U23(x1) status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U12 n__s U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U35(x1,x2) status: x1 U72(x1,x2) status: x2 #U13(x1,x2,x3) status: [x2] precedence above: #U72 #U83 #isNat #U82 #U81 #plus #activate #U14 #U22 #U84 #U71 #isNatKind U34(x1,x2,x3) status: x1 #U103(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 #U101 activate #U82 #U104 U71 #U81 #plus U101 #activate U103 U84 U23 #U13 U12 x n__s U104 #U12 U83 0 #U14 #U102 #x n__plus U32 n__0 U14 isNat n__x plus U15 #U11 U31 U92 U102 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U12(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 n__s U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U33(x1,x2,x3) status: [x2] precedence above: x(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 #U101 activate #U82 #U104 U71 #U81 #plus U101 #activate U103 U84 U23 #U13 #U103 U12 n__s U104 #U12 U83 0 #U14 #U102 #x n__plus U32 n__0 U14 isNat n__x plus U15 #U11 U31 U92 U102 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U16(x1) status: [] precedence above: n__s(x1) status: [x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 U12 U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U104(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 #U101 activate #U82 #U104 U71 #U81 #plus U101 #activate U103 U84 U23 #U13 #U103 U12 x n__s #U12 U83 0 #U14 #U102 #x n__plus U32 n__0 U14 isNat n__x plus U15 #U11 U31 U92 U102 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U42(x1) status: [] precedence above: #U12(x1,x2,x3) status: [x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 #U13 U12 n__s #U14 U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U62(x1) status: [] precedence above: U83(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U84 U23 #U13 U12 n__s #U12 #U14 n__plus U32 U14 isNat plus #U11 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 0() status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 U71 #U81 #plus #activate U23 U12 n__s U32 n__0 U14 isNat U15 #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U14(x1,x2,x3) status: [x2] precedence above: #U72 #U83 #isNat #U82 #U81 #plus #activate #U13 #U22 #U84 #U71 #isNatKind #U36(x1) status: [] precedence above: U36(x1) status: x1 #U102(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 #U101 activate #U82 #U104 U71 #U81 #plus U101 #activate U103 U84 U23 #U13 #U103 U12 x n__s U104 #U12 U83 0 #U14 #x n__plus U32 n__0 U14 isNat n__x plus U15 #U11 U31 U92 U102 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #x(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 #U101 activate #U82 #U104 U71 #U81 #plus U101 #activate U103 U84 U23 #U13 #U103 U12 x n__s U104 #U12 U83 0 #U14 #U102 n__plus U32 n__0 U14 isNat n__x plus U15 #U11 U31 U92 U102 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #s(x1) status: [] precedence above: U62(x1) status: x1 n__plus(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U84 U23 #U13 U12 n__s #U12 U83 #U14 U32 U14 isNat plus #U11 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U15(x1,x2) status: [x1] precedence above: U32(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 U12 n__s U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U33(x1,x2,x3) status: x1 n__0() status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 U71 #U81 #plus #activate U23 U12 n__s 0 U32 U14 isNat U15 #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U34(x1,x2,x3) status: [] precedence above: U14(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 U12 n__s U32 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 isNat(x1) status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 U12 n__s U32 U14 #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 n__x(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 #U101 activate #U82 #U104 U71 #U81 #plus U101 #activate U103 U84 U23 #U13 #U103 U12 x n__s U104 #U12 U83 0 #U14 #U102 #x n__plus U32 n__0 U14 isNat plus U15 #U11 U31 U92 U102 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 plus(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U84 U23 #U13 U12 n__s #U12 U83 #U14 n__plus U32 U14 isNat #U11 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U15(x1,x2) status: x1 U61(x1,x2) status: x1 #U51(x1) status: [] precedence above: #U11(x1,x2,x3) status: [x2] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 #U13 U12 n__s #U12 #U14 U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U31(x1,x2,x3) status: x1 U92(x1) status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 U71 #U81 #plus #activate U23 U12 n__s 0 U32 n__0 U14 isNat U15 #U21 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U41(x1,x2) status: [x1,x2] precedence above: U102(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat U91 #U101 activate #U82 #U104 U71 #U81 #plus U101 #activate U103 U84 U23 #U13 #U103 U12 x n__s U104 #U12 U83 0 #U14 #U102 #x n__plus U32 n__0 U14 isNat n__x plus U15 #U11 U31 U92 #U21 U81 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U21(x1,x2) status: [x2] precedence above: #U72 #U83 #isNat #U82 #U81 #plus #activate #U22 #U84 #U71 #isNatKind U81(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U84 U23 #U13 U12 n__s #U12 U83 #U14 n__plus U32 U14 isNat plus #U11 #U21 U82 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 U82(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U84 U23 #U13 U12 n__s #U12 U83 #U14 n__plus U32 U14 isNat plus #U11 #U21 U81 #U22 tt #U84 #U71 U13 U22 #isNatKind U41 #U22(x1,x2) status: [x2] precedence above: #U72 #U83 #isNat #U82 #U81 #plus #activate #U84 #U71 #isNatKind tt() status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 U12 n__s U32 U14 isNat #U21 #U22 #U84 #U71 U13 U22 #isNatKind U41 #U84(x1,x2,x3) status: [x3,x2] precedence above: #U72 #U83 #isNat #U82 #U81 #plus #activate #U71 #isNatKind #U71(x1,x2) status: [x2,x1] precedence above: #U72 #U83 #isNat #U82 #U81 #plus #activate #U84 #isNatKind U13(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 U12 n__s U32 U14 isNat #U21 #U22 tt #U84 #U71 U22 #isNatKind U41 U22(x1,x2) status: [] precedence above: #U72 isNatKind U16 U21 #U83 U11 s #isNat #U82 #U81 #plus #activate U23 U12 n__s U32 U14 isNat #U21 #U22 tt #U84 #U71 U13 #isNatKind U41 U51(x1) status: x1 #isNatKind(x1) status: [x1] precedence above: U41(x1,x2) status: x1 #U31(x1,x2,x3) status: [x1] precedence above: #U91(x1,x2) status: [x2] precedence above: #U61(x1,x2) status: [x1,x2] precedence above: Usable rules: { 1..53 } Removed DPs: #8..10 #12..17 #19 #20 #22 #23 #25 #28 #38..41 #46 #47 #58 #60 #63..65 #72 #75..80 #82 #85 #86 #88..92 #98 #104 #126 #127 #134 #135 #139 Number of SCCs: 0, DPs: 0, edges: 0 YES