MAYBE Problem: din(der(plus(X,Y))) -> u21(din(der(X)),X,Y) u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX) u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY)) din(der(times(X,Y))) -> u31(din(der(X)),X,Y) u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX) u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX))) din(der(der(X))) -> u41(din(der(X)),X) u41(dout(DX),X) -> u42(din(der(DX)),X,DX) u42(dout(DDX),X,DX) -> dout(DDX) Proof: DP Processor: DPs: din#(der(plus(X,Y))) -> din#(der(X)) din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) u21#(dout(DX),X,Y) -> din#(der(Y)) u21#(dout(DX),X,Y) -> u22#(din(der(Y)),X,Y,DX) din#(der(times(X,Y))) -> din#(der(X)) din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) u31#(dout(DX),X,Y) -> din#(der(Y)) u31#(dout(DX),X,Y) -> u32#(din(der(Y)),X,Y,DX) din#(der(der(X))) -> din#(der(X)) din#(der(der(X))) -> u41#(din(der(X)),X) u41#(dout(DX),X) -> din#(der(DX)) u41#(dout(DX),X) -> u42#(din(der(DX)),X,DX) TRS: din(der(plus(X,Y))) -> u21(din(der(X)),X,Y) u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX) u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY)) din(der(times(X,Y))) -> u31(din(der(X)),X,Y) u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX) u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX))) din(der(der(X))) -> u41(din(der(X)),X) u41(dout(DX),X) -> u42(din(der(DX)),X,DX) u42(dout(DDX),X,DX) -> dout(DDX) TDG Processor: DPs: din#(der(plus(X,Y))) -> din#(der(X)) din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) u21#(dout(DX),X,Y) -> din#(der(Y)) u21#(dout(DX),X,Y) -> u22#(din(der(Y)),X,Y,DX) din#(der(times(X,Y))) -> din#(der(X)) din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) u31#(dout(DX),X,Y) -> din#(der(Y)) u31#(dout(DX),X,Y) -> u32#(din(der(Y)),X,Y,DX) din#(der(der(X))) -> din#(der(X)) din#(der(der(X))) -> u41#(din(der(X)),X) u41#(dout(DX),X) -> din#(der(DX)) u41#(dout(DX),X) -> u42#(din(der(DX)),X,DX) TRS: din(der(plus(X,Y))) -> u21(din(der(X)),X,Y) u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX) u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY)) din(der(times(X,Y))) -> u31(din(der(X)),X,Y) u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX) u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX))) din(der(der(X))) -> u41(din(der(X)),X) u41(dout(DX),X) -> u42(din(der(DX)),X,DX) u42(dout(DDX),X,DX) -> dout(DDX) graph: u41#(dout(DX),X) -> din#(der(DX)) -> din#(der(der(X))) -> u41#(din(der(X)),X) u41#(dout(DX),X) -> din#(der(DX)) -> din#(der(der(X))) -> din#(der(X)) u41#(dout(DX),X) -> din#(der(DX)) -> din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) u41#(dout(DX),X) -> din#(der(DX)) -> din#(der(times(X,Y))) -> din#(der(X)) u41#(dout(DX),X) -> din#(der(DX)) -> din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) u41#(dout(DX),X) -> din#(der(DX)) -> din#(der(plus(X,Y))) -> din#(der(X)) u31#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(der(X))) -> u41#(din(der(X)),X) u31#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(der(X))) -> din#(der(X)) u31#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) u31#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(times(X,Y))) -> din#(der(X)) u31#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) u31#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(plus(X,Y))) -> din#(der(X)) u21#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(der(X))) -> u41#(din(der(X)),X) u21#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(der(X))) -> din#(der(X)) u21#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) u21#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(times(X,Y))) -> din#(der(X)) u21#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) u21#(dout(DX),X,Y) -> din#(der(Y)) -> din#(der(plus(X,Y))) -> din#(der(X)) din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) -> u31#(dout(DX),X,Y) -> u32#(din(der(Y)),X,Y,DX) din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) -> u31#(dout(DX),X,Y) -> din#(der(Y)) din#(der(times(X,Y))) -> din#(der(X)) -> din#(der(der(X))) -> u41#(din(der(X)),X) din#(der(times(X,Y))) -> din#(der(X)) -> din#(der(der(X))) -> din#(der(X)) din#(der(times(X,Y))) -> din#(der(X)) -> din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) din#(der(times(X,Y))) -> din#(der(X)) -> din#(der(times(X,Y))) -> din#(der(X)) din#(der(times(X,Y))) -> din#(der(X)) -> din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) din#(der(times(X,Y))) -> din#(der(X)) -> din#(der(plus(X,Y))) -> din#(der(X)) din#(der(der(X))) -> u41#(din(der(X)),X) -> u41#(dout(DX),X) -> u42#(din(der(DX)),X,DX) din#(der(der(X))) -> u41#(din(der(X)),X) -> u41#(dout(DX),X) -> din#(der(DX)) din#(der(der(X))) -> din#(der(X)) -> din#(der(der(X))) -> u41#(din(der(X)),X) din#(der(der(X))) -> din#(der(X)) -> din#(der(der(X))) -> din#(der(X)) din#(der(der(X))) -> din#(der(X)) -> din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) din#(der(der(X))) -> din#(der(X)) -> din#(der(times(X,Y))) -> din#(der(X)) din#(der(der(X))) -> din#(der(X)) -> din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) din#(der(der(X))) -> din#(der(X)) -> din#(der(plus(X,Y))) -> din#(der(X)) din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) -> u21#(dout(DX),X,Y) -> u22#(din(der(Y)),X,Y,DX) din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) -> u21#(dout(DX),X,Y) -> din#(der(Y)) din#(der(plus(X,Y))) -> din#(der(X)) -> din#(der(der(X))) -> u41#(din(der(X)),X) din#(der(plus(X,Y))) -> din#(der(X)) -> din#(der(der(X))) -> din#(der(X)) din#(der(plus(X,Y))) -> din#(der(X)) -> din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) din#(der(plus(X,Y))) -> din#(der(X)) -> din#(der(times(X,Y))) -> din#(der(X)) din#(der(plus(X,Y))) -> din#(der(X)) -> din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) din#(der(plus(X,Y))) -> din#(der(X)) -> din#(der(plus(X,Y))) -> din#(der(X)) Restore Modifier: DPs: din#(der(plus(X,Y))) -> din#(der(X)) din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) u21#(dout(DX),X,Y) -> din#(der(Y)) u21#(dout(DX),X,Y) -> u22#(din(der(Y)),X,Y,DX) din#(der(times(X,Y))) -> din#(der(X)) din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) u31#(dout(DX),X,Y) -> din#(der(Y)) u31#(dout(DX),X,Y) -> u32#(din(der(Y)),X,Y,DX) din#(der(der(X))) -> din#(der(X)) din#(der(der(X))) -> u41#(din(der(X)),X) u41#(dout(DX),X) -> din#(der(DX)) u41#(dout(DX),X) -> u42#(din(der(DX)),X,DX) TRS: din(der(plus(X,Y))) -> u21(din(der(X)),X,Y) u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX) u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY)) din(der(times(X,Y))) -> u31(din(der(X)),X,Y) u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX) u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX))) din(der(der(X))) -> u41(din(der(X)),X) u41(dout(DX),X) -> u42(din(der(DX)),X,DX) u42(dout(DDX),X,DX) -> dout(DDX) SCC Processor: #sccs: 1 #rules: 9 #arcs: 42/144 DPs: u41#(dout(DX),X) -> din#(der(DX)) din#(der(plus(X,Y))) -> din#(der(X)) din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) u21#(dout(DX),X,Y) -> din#(der(Y)) din#(der(times(X,Y))) -> din#(der(X)) din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) u31#(dout(DX),X,Y) -> din#(der(Y)) din#(der(der(X))) -> din#(der(X)) din#(der(der(X))) -> u41#(din(der(X)),X) TRS: din(der(plus(X,Y))) -> u21(din(der(X)),X,Y) u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX) u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY)) din(der(times(X,Y))) -> u31(din(der(X)),X,Y) u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX) u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX))) din(der(der(X))) -> u41(din(der(X)),X) u41(dout(DX),X) -> u42(din(der(DX)),X,DX) u42(dout(DDX),X,DX) -> dout(DDX) Open