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 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(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, edges: 999 SCC { #1..33 #35 #37..42 #44 #45 #47 #48 #50..56 #58..63 #65..68 #70..76 #78..105 #107..144 #146 #147 } 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{0, x3, x2} isNatKind(x1) weight: 2 U16(x1) weight: 0 U21(x1,x2) weight: 0 #U83(x1,x2,x3) weight: max{0, x3, x2} U11(x1,x2,x3) weight: 0 s(x1) weight: x1 #isNat(x1) weight: x1 U42(x1) weight: 0 U91(x1,x2) weight: 0 #U35(x1,x2) weight: max{0, x2} #U101(x1,x2,x3) weight: max{0, 16 + x3, x2} activate(x1) weight: x1 #U82(x1,x2,x3) weight: max{0, x3, x2} #U104(x1,x2,x3) weight: max{0, 16 + x3, x2} U71(x1,x2) weight: max{x2, (/ 15 2) + x1} #U81(x1,x2,x3) weight: max{0, x3, x2} #U92(x1) weight: 0 #plus(x1,x2) weight: max{x2, x1} U101(x1,x2,x3) weight: max{0, 16 + x3, x2} #activate(x1) weight: x1 U103(x1,x2,x3) weight: max{0, 16 + x3, x2} #U23(x1) weight: 0 U84(x1,x2,x3) weight: max{0, x3, 16 + x2} U23(x1) weight: 0 U35(x1,x2) weight: 0 U72(x1,x2) weight: max{x2, (/ 1 2) + x1} #U13(x1,x2,x3) weight: max{10 + x3, x2, 11 + x1} U34(x1,x2,x3) weight: max{0, (/ 1 2) + x1} #U103(x1,x2,x3) weight: max{0, 16 + x3, x2} U12(x1,x2,x3) weight: 0 #U33(x1,x2,x3) weight: max{0, x3, x2} x(x1,x2) weight: max{x2, 16 + x1} #U16(x1) weight: 0 n__s(x1) weight: x1 U104(x1,x2,x3) weight: max{0, 16 + x3, x2} #U42(x1) weight: 0 #U12(x1,x2,x3) weight: max{0, (/ 27 2) + x3, x2} #U62(x1) weight: 0 U83(x1,x2,x3) weight: max{0, x3, 16 + x2} 0() weight: 0 #U14(x1,x2,x3) weight: max{(/ 19 2) + x3, x2, (/ 17 2) + x1} #U36(x1) weight: 0 U36(x1) weight: 0 #U102(x1,x2,x3) weight: max{0, 16 + x3, x2} #x(x1,x2) weight: max{x2, 16 + x1} #s(x1) weight: 0 U62(x1) weight: 0 n__plus(x1,x2) weight: max{16 + x2, x1} #U15(x1,x2) weight: max{x2, (/ 1 2) + x1} U32(x1,x2,x3) weight: max{0, (/ 9 2) + x1} U33(x1,x2,x3) weight: max{0, (/ 5 2) + x1} n__0() weight: 0 #U34(x1,x2,x3) weight: max{0, x3, x2} U14(x1,x2,x3) weight: 0 isNat(x1) weight: (/ 17 2) n__x(x1,x2) weight: max{x2, 16 + x1} plus(x1,x2) weight: max{16 + x2, x1} U15(x1,x2) weight: 0 U61(x1,x2) weight: 0 #U51(x1) weight: 0 #U11(x1,x2,x3) weight: max{(/ 27 2) + x3, x2, 14 + x1} U31(x1,x2,x3) weight: max{0, (/ 13 2) + x1} U92(x1) weight: 0 #U41(x1,x2) weight: max{x2, 14 + x1} U102(x1,x2,x3) weight: max{0, 16 + x3, x2} #U21(x1,x2) weight: max{0, x2} U81(x1,x2,x3) weight: max{x3, 16 + x2, (/ 1 2) + x1} U82(x1,x2,x3) weight: max{x3, 16 + x2, (/ 1 2) + x1} #U22(x1,x2) weight: max{0, x2} tt() weight: 0 #U84(x1,x2,x3) weight: max{0, x3, x2} #U71(x1,x2) weight: max{0, x2} U13(x1,x2,x3) weight: 0 U22(x1,x2) weight: 0 U51(x1) weight: 0 #isNatKind(x1) weight: x1 U41(x1,x2) weight: 0 #U31(x1,x2,x3) weight: max{0, x3, x2} #U91(x1,x2) weight: max{x2, (/ 15 2) + x1} #U61(x1,x2) weight: max{0, x2} Usable rules: { 1..53 } Removed DPs: #2 #3 #5 #7 #24 #26 #27 #29 #31 #32 #62 #73 #74 #76 #84 #96 #109..111 #119 #120 #122 #127 #128 #131 #139 #141 #144 Number of SCCs: 1, DPs: 106, edges: 552 SCC { #1 #4 #6 #8..23 #25 #28 #30 #33 #35 #39..42 #44 #45 #47 #48 #50..56 #58..61 #63 #65..68 #70..72 #75 #78..83 #85..95 #97..105 #107 #108 #112..118 #121 #123..126 #129 #130 #132..138 #140 #142 #143 #146 #147 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded. #0() weight: 0 #U72(x1,x2) weight: max{0, (/ 3 16) + x2} #U32(x1,x2,x3) weight: max{0, (/ 3 16) + x3, (/ 5 8) + x2} isNatKind(x1) weight: (/ 1 16) U16(x1) weight: 0 U21(x1,x2) weight: 0 #U83(x1,x2,x3) weight: max{0, (/ 3 16) + x3, (/ 5 8) + x2} U11(x1,x2,x3) weight: 0 s(x1) weight: x1 #isNat(x1) weight: (/ 3 16) + x1 U42(x1) weight: 0 U91(x1,x2) weight: 0 #U35(x1,x2) weight: max{(/ 3 16) + x2, (/ 1 4) + x1} #U101(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 3 16) + x2} activate(x1) weight: x1 #U82(x1,x2,x3) weight: max{0, (/ 3 16) + x3, (/ 5 8) + x2} #U104(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 3 16) + x2} U71(x1,x2) weight: max{x2, (/ 1 8) + x1} #U81(x1,x2,x3) weight: max{0, (/ 3 16) + x3, (/ 5 8) + x2} #U92(x1) weight: 0 #plus(x1,x2) weight: max{(/ 5 8) + x2, (/ 3 16) + x1} U101(x1,x2,x3) weight: max{0, (/ 7 16) + x3, x2} #activate(x1) weight: (/ 3 16) + x1 U103(x1,x2,x3) weight: max{0, (/ 7 16) + x3, x2} #U23(x1) weight: 0 U84(x1,x2,x3) weight: max{0, x3, (/ 7 16) + x2} U23(x1) weight: 0 U35(x1,x2) weight: 0 U72(x1,x2) weight: max{x2, (/ 1 16) + x1} #U13(x1,x2,x3) weight: max{(/ 5 8) + x3, (/ 3 16) + x2, (/ 9 16) + x1} U34(x1,x2,x3) weight: max{0, (/ 1 16) + x1} #U103(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 3 16) + x2} U12(x1,x2,x3) weight: 0 #U33(x1,x2,x3) weight: max{0, (/ 3 16) + x3, (/ 5 8) + x2} x(x1,x2) weight: max{x2, (/ 7 16) + x1} #U16(x1) weight: 0 n__s(x1) weight: x1 U104(x1,x2,x3) weight: max{0, (/ 7 16) + x3, x2} #U42(x1) weight: 0 #U12(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 3 16) + x2} #U62(x1) weight: 0 U83(x1,x2,x3) weight: max{0, x3, (/ 7 16) + x2} 0() weight: 0 #U14(x1,x2,x3) weight: max{(/ 5 8) + x3, (/ 3 16) + x2, (/ 9 16) + x1} #U36(x1) weight: 0 U36(x1) weight: 0 #U102(x1,x2,x3) weight: max{0, (/ 5 8) + x3, (/ 3 16) + x2} #x(x1,x2) weight: max{(/ 3 16) + x2, (/ 5 8) + x1} #s(x1) weight: 0 U62(x1) weight: 0 n__plus(x1,x2) weight: max{(/ 7 16) + x2, x1} #U15(x1,x2) weight: max{x2, (/ 1 16) + x1} U32(x1,x2,x3) weight: max{0, (/ 3 16) + x1} U33(x1,x2,x3) weight: max{0, (/ 1 8) + x1} n__0() weight: 0 #U34(x1,x2,x3) weight: max{0, (/ 3 16) + x3, (/ 5 8) + x2} U14(x1,x2,x3) weight: 0 isNat(x1) weight: (/ 5 16) n__x(x1,x2) weight: max{x2, (/ 7 16) + x1} plus(x1,x2) weight: max{(/ 7 16) + x2, x1} U15(x1,x2) weight: 0 U61(x1,x2) weight: 0 #U51(x1) weight: 0 #U11(x1,x2,x3) weight: max{(/ 5 8) + x3, (/ 3 16) + x2, (/ 9 16) + x1} U31(x1,x2,x3) weight: max{0, (/ 1 4) + x1} U92(x1) weight: 0 #U41(x1,x2) weight: max{(/ 1 4) + x2, (/ 1 16) + x1} U102(x1,x2,x3) weight: max{0, (/ 7 16) + x3, x2} #U21(x1,x2) weight: max{0, (/ 3 16) + x2} U81(x1,x2,x3) weight: max{x3, (/ 7 16) + x2, (/ 1 16) + x1} U82(x1,x2,x3) weight: max{x3, (/ 7 16) + x2, (/ 1 16) + x1} #U22(x1,x2) weight: max{0, (/ 3 16) + x2} tt() weight: 0 #U84(x1,x2,x3) weight: max{0, (/ 3 16) + x3, (/ 5 8) + x2} #U71(x1,x2) weight: max{0, (/ 3 16) + x2} U13(x1,x2,x3) weight: 0 U22(x1,x2) weight: 0 U51(x1) weight: 0 #isNatKind(x1) weight: (/ 3 16) + x1 U41(x1,x2) weight: 0 #U31(x1,x2,x3) weight: max{0, (/ 3 16) + x3, (/ 5 8) + x2} #U91(x1,x2) weight: max{(/ 1 4) + x2, (/ 1 4) + x1} #U61(x1,x2) weight: max{0, (/ 3 16) + x2} Usable rules: { 1..53 } Removed DPs: #6 #11 #18 #21 #50 #51 #53..55 #60 #70 #71 #90 #98..100 #103 #104 #116 #135 Number of SCCs: 1, DPs: 86, edges: 410 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 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #0() weight: 0 #U72(x1,x2) weight: x2 #U32(x1,x2,x3) weight: (/ 5 8) + x3 isNatKind(x1) weight: (/ 1 8) U16(x1) weight: (/ 3 4) + x1 U21(x1,x2) weight: (/ 1 8) + x1 #U83(x1,x2,x3) weight: x3 U11(x1,x2,x3) weight: (/ 1 4) s(x1) weight: x1 #isNat(x1) weight: x1 U42(x1) weight: 0 U91(x1,x2) weight: 0 #U35(x1,x2) weight: (/ 1 8) + x2 #U101(x1,x2,x3) weight: (/ 7 8) + x2 activate(x1) weight: x1 #U82(x1,x2,x3) weight: x3 #U104(x1,x2,x3) weight: (/ 7 8) + x2 U71(x1,x2) weight: x2 #U81(x1,x2,x3) weight: x3 #U92(x1) weight: 0 #plus(x1,x2) weight: x1 U101(x1,x2,x3) weight: (/ 7 8) + x2 #activate(x1) weight: x1 U103(x1,x2,x3) weight: (/ 7 8) + x2 #U23(x1) weight: 0 U84(x1,x2,x3) weight: x3 U23(x1) weight: (/ 1 4) + x1 U35(x1,x2) weight: (/ 5 8) + x1 U72(x1,x2) weight: x2 #U13(x1,x2,x3) weight: x2 U34(x1,x2,x3) weight: (/ 5 8) #U103(x1,x2,x3) weight: (/ 7 8) + x2 U12(x1,x2,x3) weight: (/ 3 8) #U33(x1,x2,x3) weight: (/ 1 2) + x3 x(x1,x2) weight: (/ 7 8) + x2 #U16(x1) weight: 0 n__s(x1) weight: x1 U104(x1,x2,x3) weight: (/ 7 8) + x2 #U42(x1) weight: 0 #U12(x1,x2,x3) weight: x2 #U62(x1) weight: 0 U83(x1,x2,x3) weight: x3 0() weight: 0 #U14(x1,x2,x3) weight: x2 #U36(x1) weight: 0 U36(x1) weight: (/ 3 4) #U102(x1,x2,x3) weight: (/ 7 8) + x2 #x(x1,x2) weight: (/ 7 8) + x2 #s(x1) weight: 0 U62(x1) weight: x1 n__plus(x1,x2) weight: x1 #U15(x1,x2) weight: (/ 1 8) U32(x1,x2,x3) weight: (/ 3 8) U33(x1,x2,x3) weight: (/ 1 2) n__0() weight: 0 #U34(x1,x2,x3) weight: (/ 1 4) + x1 + x3 U14(x1,x2,x3) weight: (/ 5 8) + x3 isNat(x1) weight: (/ 1 8) n__x(x1,x2) weight: (/ 7 8) + x2 plus(x1,x2) weight: x1 U15(x1,x2) weight: (/ 3 4) U61(x1,x2) weight: (/ 1 8) #U51(x1) weight: 0 #U11(x1,x2,x3) weight: x2 U31(x1,x2,x3) weight: (/ 1 4) U92(x1) weight: 0 #U41(x1,x2) weight: 0 U102(x1,x2,x3) weight: (/ 7 8) + x2 #U21(x1,x2) weight: x2 U81(x1,x2,x3) weight: x3 U82(x1,x2,x3) weight: x3 #U22(x1,x2) weight: x2 tt() weight: 0 #U84(x1,x2,x3) weight: x3 #U71(x1,x2) weight: x2 U13(x1,x2,x3) weight: (/ 1 2) U22(x1,x2) weight: (/ 1 4) + x2 U51(x1) weight: 0 #isNatKind(x1) weight: x1 U41(x1,x2) weight: x1 #U31(x1,x2,x3) weight: (/ 3 4) + x3 #U91(x1,x2) weight: 0 #U61(x1,x2) weight: (/ 1 8) + x1 + x2 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, edges: 213 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 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded. #0() status: [] precedence above: #U72(x1,x2) status: x2 #U32(x1,x2,x3) status: [x3] precedence above: isNatKind(x1) status: [] precedence above: #U72 U16 U11 s U91 activate U23 n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 U16(x1) status: [] precedence above: #U72 isNatKind U11 s U91 activate U23 n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 U21(x1,x2) status: x1 #U83(x1,x2,x3) status: x3 U11(x1,x2,x3) status: x1 s(x1) status: [x1] precedence above: #U72 isNatKind U16 U11 U91 activate U23 n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 #isNat(x1) status: x1 U42(x1) status: x1 U91(x1,x2) status: [] precedence above: #U72 isNatKind U16 U11 s activate U23 n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 #U35(x1,x2) status: [x2,x1] precedence above: #U101(x1,x2,x3) status: [x3,x2] precedence above: #U72 isNatKind U16 U21 U11 s U91 activate #U104 U71 U101 U103 U84 U23 U72 #U13 #U103 x n__s U104 #U12 U83 0 #U102 #x U62 n__plus n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 activate(x1) status: x1 #U82(x1,x2,x3) status: x3 #U104(x1,x2,x3) status: [x3,x2] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate U71 U101 U103 U84 U23 U72 #U13 #U103 x n__s U104 #U12 U83 0 #U102 #x U62 n__plus n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 U71(x1,x2) status: [x1,x2] precedence above: U72 #U81(x1,x2,x3) status: x3 #U92(x1) status: [] precedence above: #plus(x1,x2) status: x1 U101(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U103 U84 U23 U72 #U13 #U103 x n__s U104 #U12 U83 0 #U102 #x U62 n__plus n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 #activate(x1) status: x1 U103(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U84 U23 U72 #U13 #U103 x n__s U104 #U12 U83 0 #U102 #x U62 n__plus n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 #U23(x1) status: [] precedence above: U84(x1,x2,x3) status: [x2,x3,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U23 U72 #U13 n__s #U12 U83 0 U62 n__plus n__0 U14 isNat plus U15 U61 #U11 U31 #U21 U81 U82 #U22 tt U22 U51 #isNatKind U23(x1) status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 U35(x1,x2) status: x1 U72(x1,x2) status: [x1,x2] precedence above: #U13(x1,x2,x3) status: [x2] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 U34(x1,x2,x3) status: x1 #U103(x1,x2,x3) status: [x3,x2] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U72 #U13 x n__s U104 #U12 U83 0 #U102 #x U62 n__plus n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 U12(x1,x2,x3) status: x1 #U33(x1,x2,x3) status: [x3] precedence above: x(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U72 #U13 #U103 n__s U104 #U12 U83 0 #U102 #x U62 n__plus n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 #U16(x1) status: [] precedence above: n__s(x1) status: [x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 U104(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U72 #U13 #U103 x n__s #U12 U83 0 #U102 #x U62 n__plus n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 #U42(x1) status: [] precedence above: #U12(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 #U13 n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 #U62(x1) status: [] precedence above: U83(x1,x2,x3) status: [x2,x3,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U84 U23 U72 #U13 n__s #U12 0 U62 n__plus n__0 U14 isNat plus U15 U61 #U11 U31 #U21 U81 U82 #U22 tt U22 U51 #isNatKind 0() status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 #U14(x1,x2,x3) status: x2 #U36(x1) status: [] precedence above: U36(x1) status: x1 #U102(x1,x2,x3) status: [x3,x2] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U72 #U13 #U103 x n__s U104 #U12 U83 0 #x U62 n__plus n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 #x(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U72 #U13 #U103 x n__s U104 #U12 U83 0 #U102 U62 n__plus n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 #s(x1) status: [] precedence above: U62(x1) status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 n__plus(x1,x2) status: [x2,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U84 U23 U72 #U13 n__s #U12 U83 0 U62 n__0 U14 isNat plus U15 U61 #U11 U31 #U21 U81 U82 #U22 tt U22 U51 #isNatKind #U15(x1,x2) status: [x2] precedence above: U32(x1,x2,x3) status: x1 U33(x1,x2,x3) status: x1 n__0() status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 #U34(x1,x2,x3) status: [x1,x3] precedence above: U14(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 n__0 isNat U15 U61 U31 #U21 #U22 tt U22 U51 isNat(x1) status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 n__0 U14 U15 U61 U31 #U21 #U22 tt U22 U51 n__x(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U72 #U13 #U103 x n__s U104 #U12 U83 0 #U102 #x U62 n__plus n__0 U14 isNat plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 plus(x1,x2) status: [x2,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U84 U23 U72 #U13 n__s #U12 U83 0 U62 n__plus n__0 U14 isNat U15 U61 #U11 U31 #U21 U81 U82 #U22 tt U22 U51 #isNatKind U15(x1,x2) status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 n__0 U14 isNat U61 U31 #U21 #U22 tt U22 U51 U61(x1,x2) status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 n__0 U14 isNat U15 U31 #U21 #U22 tt U22 U51 #U51(x1) status: [] precedence above: #U11(x1,x2,x3) status: [x2,x3] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U23 U72 #U13 n__s #U12 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 U51 #isNatKind U31(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 n__0 U14 isNat U15 U61 #U21 #U22 tt U22 U51 U92(x1) status: x1 #U41(x1,x2) status: [x1] precedence above: U102(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U72 #U13 #U103 x n__s U104 #U12 U83 0 #U102 #x U62 n__plus n__0 U14 isNat n__x plus U15 U61 #U11 U31 #U21 U81 U82 #U22 tt #U84 U22 U51 #isNatKind U41 #U21(x1,x2) status: [x2] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U22 tt U22 U51 U81(x1,x2,x3) status: [x2,x3,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U84 U23 U72 #U13 n__s #U12 U83 0 U62 n__plus n__0 U14 isNat plus U15 U61 #U11 U31 #U21 U82 #U22 tt U22 U51 #isNatKind U82(x1,x2,x3) status: [x2,x3,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U84 U23 U72 #U13 n__s #U12 U83 0 U62 n__plus n__0 U14 isNat plus U15 U61 #U11 U31 #U21 U81 #U22 tt U22 U51 #isNatKind #U22(x1,x2) status: [x1,x2] precedence above: tt() status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 U22 U51 #U84(x1,x2,x3) status: x3 #U71(x1,x2) status: x2 U13(x1,x2,x3) status: x1 U22(x1,x2) status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U51 U51(x1) status: [] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 n__s 0 U62 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U22 #isNatKind(x1) status: x1 U41(x1,x2) status: x1 #U31(x1,x2,x3) status: [x1] precedence above: #U91(x1,x2) status: [x2] precedence above: #U61(x1,x2) status: [x2] precedence above: Usable rules: { 1..53 } Removed DPs: #14..16 #22 #23 #25 #28 #35 #39..42 #47 #48 #72 #75 #78..83 #85 #92..95 #142 #143 Number of SCCs: 1, DPs: 5, edges: 5 SCC { #8 #17 #58 #87 #97 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded. #0() status: [] precedence above: #U72(x1,x2) status: [] precedence above: #U32(x1,x2,x3) status: [x3] precedence above: isNatKind(x1) status: [] precedence above: #U72 U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 U16(x1) status: [] precedence above: #U72 isNatKind U11 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 U21(x1,x2) status: x1 #U83(x1,x2,x3) status: x2 U11(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 s(x1) status: [x1] precedence above: #U72 n__s #U21 #U22 #isNat(x1) status: [] precedence above: #activate #U71 U42(x1) status: x1 U91(x1,x2) status: [] precedence above: #U72 isNatKind U16 U11 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 #U35(x1,x2) status: [x2,x1] precedence above: #U101(x1,x2,x3) status: [x3,x2] precedence above: #U72 isNatKind U16 U21 U11 s U91 activate #U104 U71 U101 U103 U84 U23 U35 U72 #U13 U34 #U103 U12 x n__s U104 #U12 U83 0 U36 #U102 #x U62 n__plus U32 U33 n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 activate(x1) status: x1 #U82(x1,x2,x3) status: x2 #U104(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate U71 U101 U103 U84 U23 U35 U72 #U13 U34 #U103 U12 x n__s U104 #U12 U83 0 U36 #U102 #x U62 n__plus U32 U33 n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 U71(x1,x2) status: [x1,x2] precedence above: U72 #U81(x1,x2,x3) status: x2 #U92(x1) status: [] precedence above: #plus(x1,x2) status: x2 U101(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U103 U84 U23 U35 U72 #U13 U34 #U103 U12 x n__s U104 #U12 U83 0 U36 #U102 #x U62 n__plus U32 U33 n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 #activate(x1) status: x1 U103(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U84 U23 U35 U72 #U13 U34 #U103 U12 x n__s U104 #U12 U83 0 U36 #U102 #x U62 n__plus U32 U33 n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 #U23(x1) status: [] precedence above: U84(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U23 U35 U72 #U13 U34 U12 n__s #U12 U83 0 U36 U62 n__plus U32 U33 n__0 U14 isNat plus U15 U61 #U11 U31 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U23(x1) status: [] precedence above: #U72 isNatKind U16 U11 U91 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 U35(x1,x2) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 U72(x1,x2) status: [x2,x1] precedence above: #U13(x1,x2,x3) status: [x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 U35 U34 U12 n__s 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U13 U22 U51 U34(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 #U103(x1,x2,x3) status: [x1] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U35 U72 #U13 U34 U12 x n__s U104 #U12 U83 0 U36 #U102 #x U62 n__plus U32 U33 n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 U12(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 #U33(x1,x2,x3) status: [x3] precedence above: x(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U35 U72 #U13 U34 #U103 U12 n__s U104 #U12 U83 0 U36 #U102 #x U62 n__plus U32 U33 n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 #U16(x1) status: [] precedence above: n__s(x1) status: [x1] precedence above: #U72 s #U21 #U22 U104(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U35 U72 #U13 U34 #U103 U12 x n__s #U12 U83 0 U36 #U102 #x U62 n__plus U32 U33 n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 #U42(x1) status: [] precedence above: #U12(x1,x2,x3) status: [x3] precedence above: #U72 isNatKind U16 U11 s U91 activate U23 U35 #U13 U34 U12 n__s 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U13 U22 U51 #U62(x1) status: [] precedence above: U83(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U84 U23 U35 U72 #U13 U34 U12 n__s #U12 0 U36 U62 n__plus U32 U33 n__0 U14 isNat plus U15 U61 #U11 U31 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind 0() status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 #U14(x1,x2,x3) status: [x1] precedence above: #activate #U71 #U36(x1) status: [] precedence above: U36(x1) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 #U102(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U35 U72 #U13 U34 #U103 U12 x n__s U104 #U12 U83 0 U36 #x U62 n__plus U32 U33 n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 #x(x1,x2) status: [] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U35 U72 #U13 U34 #U103 U12 x n__s U104 #U12 U83 0 U36 #U102 U62 n__plus U32 U33 n__0 U14 isNat n__x plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 #s(x1) status: [] precedence above: U62(x1) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 n__plus(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U84 U23 U35 U72 #U13 U34 U12 n__s #U12 U83 0 U36 U62 U32 U33 n__0 U14 isNat plus U15 U61 #U11 U31 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind #U15(x1,x2) status: [x2] precedence above: U32(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 U33(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U32 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U22 n__0() status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 U14 isNat U15 U61 #U21 #U22 tt U13 U22 #U34(x1,x2,x3) status: [x1,x3] precedence above: U14(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 isNat U15 U61 #U21 #U22 tt U13 U22 isNat(x1) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 U15 U61 #U21 #U22 tt U13 U22 n__x(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U35 U72 #U13 U34 #U103 U12 x n__s U104 #U12 U83 0 U36 #U102 #x U62 n__plus U32 U33 n__0 U14 isNat plus U15 U61 #U11 U31 U102 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 plus(x1,x2) status: [x1,x2] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U84 U23 U35 U72 #U13 U34 U12 n__s #U12 U83 0 U36 U62 n__plus U32 U33 n__0 U14 isNat U15 U61 #U11 U31 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U15(x1,x2) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U61 #U21 #U22 tt U13 U22 U61(x1,x2) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 #U21 #U22 tt U13 U22 #U51(x1) status: [] precedence above: #U11(x1,x2,x3) status: [x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U23 U35 U72 #U13 U34 U12 n__s #U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 U31 #U21 #U22 tt U13 U22 U51 #isNatKind U31(x1,x2,x3) status: x1 U92(x1) status: x1 #U41(x1,x2) status: [x1] precedence above: U102(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U21 U11 s U91 #U101 activate #U104 U71 U101 U103 U84 U23 U35 U72 #U13 U34 #U103 U12 x n__s U104 #U12 U83 0 U36 #U102 #x U62 n__plus U32 U33 n__0 U14 isNat n__x plus U15 U61 #U11 U31 #U21 U81 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U41 #U21(x1,x2) status: [x2,x1] precedence above: #U72 #U22 U81(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U84 U23 U35 U72 #U13 U34 U12 n__s #U12 U83 0 U36 U62 n__plus U32 U33 n__0 U14 isNat plus U15 U61 #U11 U31 #U21 U82 #U22 tt #U84 U13 U22 U51 #isNatKind U82(x1,x2,x3) status: [x3,x2,x1] precedence above: #U72 isNatKind U16 U11 s U91 activate U71 U84 U23 U35 U72 #U13 U34 U12 n__s #U12 U83 0 U36 U62 n__plus U32 U33 n__0 U14 isNat plus U15 U61 #U11 U31 #U21 U81 #U22 tt #U84 U13 U22 U51 #isNatKind #U22(x1,x2) status: [] precedence above: tt() status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 U13 U22 #U84(x1,x2,x3) status: x2 #U71(x1,x2) status: x2 U13(x1,x2,x3) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U22 U22(x1,x2) status: [] precedence above: #U72 isNatKind U16 U11 U91 U23 U35 U34 U12 0 U36 U62 U32 U33 n__0 U14 isNat U15 U61 #U21 #U22 tt U13 U51(x1) status: x1 #isNatKind(x1) status: [] 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: [] precedence above: Usable rules: { 1..53 } Removed DPs: #17 Number of SCCs: 0, DPs: 0, edges: 0 YES