/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(zip(nil(),XS)) -> mark(nil()) active(zip(X,nil())) -> mark(nil()) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(tail(cons(X,XS))) -> mark(XS) active(repItems(nil())) -> mark(nil()) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0, [ok](x0) = x0, [proper](x0) = x0, [repItems](x0) = 2x0, [tail](x0) = x0 + 1, [pair](x0, x1) = x0 + x1, [zip](x0, x1) = x0 + x1, [nil] = 0, [take](x0, x1) = 2x0 + x1, [s](x0) = x0, [mark](x0) = x0, [cons](x0, x1) = 2x0 + x1, [incr](x0) = 2x0, [oddNs] = 0, [0] = 0, [active](x0) = x0, [pairNs] = 0 orientation: active(pairNs()) = 0 >= 0 = mark(cons(0(),incr(oddNs()))) active(oddNs()) = 0 >= 0 = mark(incr(pairNs())) active(incr(cons(X,XS))) = 4X + 2XS >= 2X + 2XS = mark(cons(s(X),incr(XS))) active(take(0(),XS)) = XS >= 0 = mark(nil()) active(take(s(N),cons(X,XS))) = 2N + 2X + XS >= 2N + 2X + XS = mark(cons(X,take(N,XS))) active(zip(nil(),XS)) = XS >= 0 = mark(nil()) active(zip(X,nil())) = X >= 0 = mark(nil()) active(zip(cons(X,XS),cons(Y,YS))) = 2X + XS + 2Y + YS >= 2X + XS + 2Y + YS = mark(cons(pair(X,Y),zip(XS,YS))) active(tail(cons(X,XS))) = 2X + XS + 1 >= XS = mark(XS) active(repItems(nil())) = 0 >= 0 = mark(nil()) active(repItems(cons(X,XS))) = 4X + 2XS >= 4X + 2XS = mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = cons(active(X1),X2) active(incr(X)) = 2X >= 2X = incr(active(X)) active(s(X)) = X >= X = s(active(X)) active(take(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = take(active(X1),X2) active(take(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = take(X1,active(X2)) active(zip(X1,X2)) = X1 + X2 >= X1 + X2 = zip(active(X1),X2) active(zip(X1,X2)) = X1 + X2 >= X1 + X2 = zip(X1,active(X2)) active(pair(X1,X2)) = X1 + X2 >= X1 + X2 = pair(active(X1),X2) active(pair(X1,X2)) = X1 + X2 >= X1 + X2 = pair(X1,active(X2)) active(tail(X)) = X + 1 >= X + 1 = tail(active(X)) active(repItems(X)) = 2X >= 2X = repItems(active(X)) cons(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(cons(X1,X2)) incr(mark(X)) = 2X >= 2X = mark(incr(X)) s(mark(X)) = X >= X = mark(s(X)) take(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(take(X1,X2)) take(X1,mark(X2)) = 2X1 + X2 >= 2X1 + X2 = mark(take(X1,X2)) zip(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(zip(X1,X2)) zip(X1,mark(X2)) = X1 + X2 >= X1 + X2 = mark(zip(X1,X2)) pair(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(pair(X1,X2)) pair(X1,mark(X2)) = X1 + X2 >= X1 + X2 = mark(pair(X1,X2)) tail(mark(X)) = X + 1 >= X + 1 = mark(tail(X)) repItems(mark(X)) = 2X >= 2X = mark(repItems(X)) proper(pairNs()) = 0 >= 0 = ok(pairNs()) proper(cons(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = cons(proper(X1),proper(X2)) proper(0()) = 0 >= 0 = ok(0()) proper(incr(X)) = 2X >= 2X = incr(proper(X)) proper(oddNs()) = 0 >= 0 = ok(oddNs()) proper(s(X)) = X >= X = s(proper(X)) proper(take(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = take(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(zip(X1,X2)) = X1 + X2 >= X1 + X2 = zip(proper(X1),proper(X2)) proper(pair(X1,X2)) = X1 + X2 >= X1 + X2 = pair(proper(X1),proper(X2)) proper(tail(X)) = X + 1 >= X + 1 = tail(proper(X)) proper(repItems(X)) = 2X >= 2X = repItems(proper(X)) cons(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(cons(X1,X2)) incr(ok(X)) = 2X >= 2X = ok(incr(X)) s(ok(X)) = X >= X = ok(s(X)) take(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(take(X1,X2)) zip(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(zip(X1,X2)) pair(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(pair(X1,X2)) tail(ok(X)) = X + 1 >= X + 1 = ok(tail(X)) repItems(ok(X)) = 2X >= 2X = ok(repItems(X)) top(mark(X)) = X >= X = top(proper(X)) top(ok(X)) = X >= X = top(active(X)) problem: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(zip(nil(),XS)) -> mark(nil()) active(zip(X,nil())) -> mark(nil()) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(nil())) -> mark(nil()) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 4x0, [ok](x0) = x0, [proper](x0) = x0, [repItems](x0) = 2x0, [tail](x0) = 2x0 + 5, [pair](x0, x1) = x0 + x1, [zip](x0, x1) = x0 + x1 + 4, [nil] = 2, [take](x0, x1) = x0 + 2x1 + 4, [s](x0) = x0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [incr](x0) = 4x0, [oddNs] = 0, [0] = 0, [active](x0) = x0, [pairNs] = 0 orientation: active(pairNs()) = 0 >= 0 = mark(cons(0(),incr(oddNs()))) active(oddNs()) = 0 >= 0 = mark(incr(pairNs())) active(incr(cons(X,XS))) = 4X + 4XS >= X + 4XS = mark(cons(s(X),incr(XS))) active(take(0(),XS)) = 2XS + 4 >= 2 = mark(nil()) active(take(s(N),cons(X,XS))) = N + 2X + 2XS + 4 >= N + X + 2XS + 4 = mark(cons(X,take(N,XS))) active(zip(nil(),XS)) = XS + 6 >= 2 = mark(nil()) active(zip(X,nil())) = X + 6 >= 2 = mark(nil()) active(zip(cons(X,XS),cons(Y,YS))) = X + XS + Y + YS + 4 >= X + XS + Y + YS + 4 = mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(nil())) = 4 >= 2 = mark(nil()) active(repItems(cons(X,XS))) = 2X + 2XS >= 2X + 2XS = mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(active(X1),X2) active(incr(X)) = 4X >= 4X = incr(active(X)) active(s(X)) = X >= X = s(active(X)) active(take(X1,X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = take(active(X1),X2) active(take(X1,X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = take(X1,active(X2)) active(zip(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = zip(active(X1),X2) active(zip(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = zip(X1,active(X2)) active(pair(X1,X2)) = X1 + X2 >= X1 + X2 = pair(active(X1),X2) active(pair(X1,X2)) = X1 + X2 >= X1 + X2 = pair(X1,active(X2)) active(tail(X)) = 2X + 5 >= 2X + 5 = tail(active(X)) active(repItems(X)) = 2X >= 2X = repItems(active(X)) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(cons(X1,X2)) incr(mark(X)) = 4X >= 4X = mark(incr(X)) s(mark(X)) = X >= X = mark(s(X)) take(mark(X1),X2) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = mark(take(X1,X2)) take(X1,mark(X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = mark(take(X1,X2)) zip(mark(X1),X2) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(zip(X1,X2)) zip(X1,mark(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(zip(X1,X2)) pair(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(pair(X1,X2)) pair(X1,mark(X2)) = X1 + X2 >= X1 + X2 = mark(pair(X1,X2)) tail(mark(X)) = 2X + 5 >= 2X + 5 = mark(tail(X)) repItems(mark(X)) = 2X >= 2X = mark(repItems(X)) proper(pairNs()) = 0 >= 0 = ok(pairNs()) proper(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(proper(X1),proper(X2)) proper(0()) = 0 >= 0 = ok(0()) proper(incr(X)) = 4X >= 4X = incr(proper(X)) proper(oddNs()) = 0 >= 0 = ok(oddNs()) proper(s(X)) = X >= X = s(proper(X)) proper(take(X1,X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = take(proper(X1),proper(X2)) proper(nil()) = 2 >= 2 = ok(nil()) proper(zip(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = zip(proper(X1),proper(X2)) proper(pair(X1,X2)) = X1 + X2 >= X1 + X2 = pair(proper(X1),proper(X2)) proper(tail(X)) = 2X + 5 >= 2X + 5 = tail(proper(X)) proper(repItems(X)) = 2X >= 2X = repItems(proper(X)) cons(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(cons(X1,X2)) incr(ok(X)) = 4X >= 4X = ok(incr(X)) s(ok(X)) = X >= X = ok(s(X)) take(ok(X1),ok(X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = ok(take(X1,X2)) zip(ok(X1),ok(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = ok(zip(X1,X2)) pair(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(pair(X1,X2)) tail(ok(X)) = 2X + 5 >= 2X + 5 = ok(tail(X)) repItems(ok(X)) = 2X >= 2X = ok(repItems(X)) top(mark(X)) = 4X >= 4X = top(proper(X)) top(ok(X)) = 4X >= 4X = top(active(X)) problem: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [ok](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [proper](x0) = [0 0 1]x0 [0 0 1] , [1 0 1] [repItems](x0) = [0 0 0]x0 [1 0 1] , [1 0 0] [0] [tail](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 0 0] [1 0 0] [0] [pair](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1], [1 0 0] [1 0 0] [zip](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [0 0 1] , [1] [nil] = [0] [0], [1 0 1] [1 0 0] [take](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 1] , [1 0 0] [0] [s](x0) = [0 0 1]x0 + [0] [0 0 1] [1], [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [0 0 1] , [1 0 0] [incr](x0) = [0 0 0]x0 [1 0 0] , [0] [oddNs] = [0] [0], [0] [0] = [0] [0], [1 0 0] [active](x0) = [0 0 1]x0 [0 0 1] , [0] [pairNs] = [0] [0] orientation: [0] [0] active(pairNs()) = [0] >= [0] = mark(cons(0(),incr(oddNs()))) [0] [0] [0] [0] active(oddNs()) = [0] >= [0] = mark(incr(pairNs())) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(incr(cons(X,XS))) = [1 0 0]X + [1 0 0]XS >= [0 0 0]X + [0 0 0]XS = mark(cons(s(X),incr(XS))) [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] [1] [1 0 1] [1 0 0] [1 0 0] active(take(s(N),cons(X,XS))) = [0 0 0]N + [1 0 0]X + [0 0 1]XS + [0] >= [0 0 0]N + [0 0 0]X + [0 0 0]XS = mark(cons(X,take(N,XS))) [0 0 0] [1 0 0] [0 0 1] [0] [0 0 0] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(zip(cons(X,XS),cons(Y,YS))) = [1 0 0]X + [1 0 0]XS + [1 0 0]Y + [0 0 1]YS >= [0 0 0]X + [0 0 0]XS + [0 0 0]Y + [0 0 0]YS = mark(cons(pair(X,Y),zip(XS,YS))) [1 0 0] [1 0 0] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [0 0 1] [2 0 0] [1 0 1] [2 0 0] [1 0 1] active(repItems(cons(X,XS))) = [2 0 0]X + [1 0 1]XS >= [0 0 0]X + [0 0 0]XS = mark(cons(X,cons(X,repItems(XS)))) [2 0 0] [1 0 1] [2 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(cons(X1,X2)) = [1 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(active(X1),X2) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] active(incr(X)) = [1 0 0]X >= [0 0 0]X = incr(active(X)) [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [0] active(s(X)) = [0 0 1]X + [1] >= [0 0 1]X + [0] = s(active(X)) [0 0 1] [1] [0 0 1] [1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] active(take(X1,X2)) = [0 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(active(X1),X2) [0 0 0] [0 0 1] [0 0 0] [0 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] active(take(X1,X2)) = [0 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(X1,active(X2)) [0 0 0] [0 0 1] [0 0 0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(zip(X1,X2)) = [1 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 0]X2 = zip(active(X1),X2) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(zip(X1,X2)) = [1 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 0]X2 = zip(X1,active(X2)) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] active(pair(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = pair(active(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] active(pair(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = pair(X1,active(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] active(tail(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = tail(active(X)) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1 0 1] active(repItems(X)) = [1 0 1]X >= [0 0 0]X = repItems(active(X)) [1 0 1] [1 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(cons(X1,X2)) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] incr(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(incr(X)) [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [0] s(mark(X)) = [0 0 1]X + [0] >= [0 0 0]X + [0] = mark(s(X)) [0 0 1] [1] [0 0 1] [1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] take(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(take(X1,X2)) [0 0 0] [0 0 1] [0 0 0] [0 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] take(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(take(X1,X2)) [0 0 0] [0 0 1] [0 0 0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] zip(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(zip(X1,X2)) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] zip(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(zip(X1,X2)) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] pair(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(pair(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] pair(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(pair(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] tail(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = mark(tail(X)) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1 0 1] repItems(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(repItems(X)) [1 0 1] [1 0 1] [0] [0] proper(pairNs()) = [0] >= [0] = ok(pairNs()) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(cons(X1,X2)) = [1 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(proper(X1),proper(X2)) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [0] [0] proper(0()) = [0] >= [0] = ok(0()) [0] [0] [1 0 0] [1 0 0] proper(incr(X)) = [1 0 0]X >= [0 0 0]X = incr(proper(X)) [1 0 0] [1 0 0] [0] [0] proper(oddNs()) = [0] >= [0] = ok(oddNs()) [0] [0] [1 0 0] [0] [1 0 0] [0] proper(s(X)) = [0 0 1]X + [1] >= [0 0 1]X + [0] = s(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] proper(take(X1,X2)) = [0 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(proper(X1),proper(X2)) [0 0 0] [0 0 1] [0 0 0] [0 0 1] [1] [1] proper(nil()) = [0] >= [0] = ok(nil()) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(zip(X1,X2)) = [1 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 0]X2 = zip(proper(X1),proper(X2)) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] proper(pair(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = pair(proper(X1),proper(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] proper(tail(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = tail(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1 0 1] proper(repItems(X)) = [1 0 1]X >= [0 0 0]X = repItems(proper(X)) [1 0 1] [1 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(cons(X1,X2)) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] incr(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(incr(X)) [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [0] s(ok(X)) = [0 0 1]X + [0] >= [0 0 0]X + [0] = ok(s(X)) [0 0 1] [1] [0 0 1] [1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] take(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(take(X1,X2)) [0 0 0] [0 0 1] [0 0 0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] zip(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(zip(X1,X2)) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] pair(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = ok(pair(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] tail(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = ok(tail(X)) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1 0 1] repItems(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(repItems(X)) [1 0 1] [1 0 1] [1 0 0] [1 0 0] top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) DP Processor: DPs: active#(pairNs()) -> incr#(oddNs()) active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(oddNs()) -> incr#(pairNs()) active#(incr(cons(X,XS))) -> incr#(XS) active#(incr(cons(X,XS))) -> s#(X) active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(repItems(cons(X,XS))) -> repItems#(XS) active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(incr(X)) -> active#(X) active#(incr(X)) -> incr#(active(X)) active#(s(X)) -> active#(X) active#(s(X)) -> s#(active(X)) active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> take#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> take#(X1,active(X2)) active#(zip(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(zip(X1,X2)) -> active#(X2) active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(pair(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(pair(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(tail(X)) -> active#(X) active#(tail(X)) -> tail#(active(X)) active#(repItems(X)) -> active#(X) active#(repItems(X)) -> repItems#(active(X)) cons#(mark(X1),X2) -> cons#(X1,X2) incr#(mark(X)) -> incr#(X) s#(mark(X)) -> s#(X) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) zip#(mark(X1),X2) -> zip#(X1,X2) zip#(X1,mark(X2)) -> zip#(X1,X2) pair#(mark(X1),X2) -> pair#(X1,X2) pair#(X1,mark(X2)) -> pair#(X1,X2) tail#(mark(X)) -> tail#(X) repItems#(mark(X)) -> repItems#(X) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(incr(X)) -> proper#(X) proper#(incr(X)) -> incr#(proper(X)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(zip(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(tail(X)) -> proper#(X) proper#(tail(X)) -> tail#(proper(X)) proper#(repItems(X)) -> proper#(X) proper#(repItems(X)) -> repItems#(proper(X)) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) incr#(ok(X)) -> incr#(X) s#(ok(X)) -> s#(X) take#(ok(X1),ok(X2)) -> take#(X1,X2) zip#(ok(X1),ok(X2)) -> zip#(X1,X2) pair#(ok(X1),ok(X2)) -> pair#(X1,X2) tail#(ok(X)) -> tail#(X) repItems#(ok(X)) -> repItems#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(pairNs()) -> incr#(oddNs()) active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(oddNs()) -> incr#(pairNs()) active#(incr(cons(X,XS))) -> incr#(XS) active#(incr(cons(X,XS))) -> s#(X) active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(repItems(cons(X,XS))) -> repItems#(XS) active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(incr(X)) -> active#(X) active#(incr(X)) -> incr#(active(X)) active#(s(X)) -> active#(X) active#(s(X)) -> s#(active(X)) active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> take#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> take#(X1,active(X2)) active#(zip(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(zip(X1,X2)) -> active#(X2) active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(pair(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(pair(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(tail(X)) -> active#(X) active#(tail(X)) -> tail#(active(X)) active#(repItems(X)) -> active#(X) active#(repItems(X)) -> repItems#(active(X)) cons#(mark(X1),X2) -> cons#(X1,X2) incr#(mark(X)) -> incr#(X) s#(mark(X)) -> s#(X) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) zip#(mark(X1),X2) -> zip#(X1,X2) zip#(X1,mark(X2)) -> zip#(X1,X2) pair#(mark(X1),X2) -> pair#(X1,X2) pair#(X1,mark(X2)) -> pair#(X1,X2) tail#(mark(X)) -> tail#(X) repItems#(mark(X)) -> repItems#(X) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(incr(X)) -> proper#(X) proper#(incr(X)) -> incr#(proper(X)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(zip(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(tail(X)) -> proper#(X) proper#(tail(X)) -> tail#(proper(X)) proper#(repItems(X)) -> proper#(X) proper#(repItems(X)) -> repItems#(proper(X)) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) incr#(ok(X)) -> incr#(X) s#(ok(X)) -> s#(X) take#(ok(X1),ok(X2)) -> take#(X1,X2) zip#(ok(X1),ok(X2)) -> zip#(X1,X2) pair#(ok(X1),ok(X2)) -> pair#(X1,X2) tail#(ok(X)) -> tail#(X) repItems#(ok(X)) -> repItems#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X)) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X) top#(ok(X)) -> active#(X) -> active#(repItems(X)) -> repItems#(active(X)) top#(ok(X)) -> active#(X) -> active#(repItems(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(tail(X)) -> tail#(active(X)) top#(ok(X)) -> active#(X) -> active#(tail(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(pair(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(pair(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(zip(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(zip(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(incr(X)) -> incr#(active(X)) top#(ok(X)) -> active#(X) -> active#(incr(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) top#(ok(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) top#(ok(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> repItems#(XS) top#(ok(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) top#(ok(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) top#(ok(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) top#(ok(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) top#(ok(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> s#(X) top#(ok(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> incr#(XS) top#(ok(X)) -> active#(X) -> active#(oddNs()) -> incr#(pairNs()) top#(ok(X)) -> active#(X) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) top#(ok(X)) -> active#(X) -> active#(pairNs()) -> incr#(oddNs()) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> top#(proper(X)) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(repItems(X)) -> repItems#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(repItems(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(tail(X)) -> tail#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(tail(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(incr(X)) -> incr#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(incr(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(repItems(X)) -> proper#(X) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(repItems(X)) -> proper#(X) -> proper#(repItems(X)) -> proper#(X) proper#(repItems(X)) -> proper#(X) -> proper#(tail(X)) -> tail#(proper(X)) proper#(repItems(X)) -> proper#(X) -> proper#(tail(X)) -> proper#(X) proper#(repItems(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(repItems(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(repItems(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(repItems(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(repItems(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(repItems(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(repItems(X)) -> proper#(X) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(repItems(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X1) proper#(repItems(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X2) proper#(repItems(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(repItems(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(repItems(X)) -> proper#(X) -> proper#(incr(X)) -> incr#(proper(X)) proper#(repItems(X)) -> proper#(X) -> proper#(incr(X)) -> proper#(X) proper#(repItems(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(repItems(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(repItems(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(repItems(X)) -> repItems#(proper(X)) -> repItems#(ok(X)) -> repItems#(X) proper#(repItems(X)) -> repItems#(proper(X)) -> repItems#(mark(X)) -> repItems#(X) proper#(tail(X)) -> proper#(X) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(tail(X)) -> proper#(X) -> proper#(repItems(X)) -> proper#(X) proper#(tail(X)) -> proper#(X) -> proper#(tail(X)) -> tail#(proper(X)) proper#(tail(X)) -> proper#(X) -> proper#(tail(X)) -> proper#(X) proper#(tail(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(tail(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(tail(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(tail(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(tail(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(tail(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(tail(X)) -> proper#(X) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(tail(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X1) proper#(tail(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X2) proper#(tail(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(tail(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(tail(X)) -> proper#(X) -> proper#(incr(X)) -> incr#(proper(X)) proper#(tail(X)) -> proper#(X) -> proper#(incr(X)) -> proper#(X) proper#(tail(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(tail(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(tail(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(tail(X)) -> tail#(proper(X)) -> tail#(ok(X)) -> tail#(X) proper#(tail(X)) -> tail#(proper(X)) -> tail#(mark(X)) -> tail#(X) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(repItems(X)) -> proper#(X) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(tail(X)) -> tail#(proper(X)) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(tail(X)) -> proper#(X) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(incr(X)) -> incr#(proper(X)) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(incr(X)) -> proper#(X) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(repItems(X)) -> proper#(X) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(tail(X)) -> tail#(proper(X)) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(tail(X)) -> proper#(X) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(incr(X)) -> incr#(proper(X)) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(incr(X)) -> proper#(X) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) -> pair#(ok(X1),ok(X2)) -> pair#(X1,X2) proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) -> pair#(X1,mark(X2)) -> pair#(X1,X2) proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) -> pair#(mark(X1),X2) -> pair#(X1,X2) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(repItems(X)) -> proper#(X) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(tail(X)) -> tail#(proper(X)) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(tail(X)) -> proper#(X) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(incr(X)) -> incr#(proper(X)) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(incr(X)) -> proper#(X) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(repItems(X)) -> proper#(X) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(tail(X)) -> tail#(proper(X)) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(tail(X)) -> proper#(X) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(incr(X)) -> incr#(proper(X)) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(incr(X)) -> proper#(X) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) -> zip#(ok(X1),ok(X2)) -> zip#(X1,X2) proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) -> zip#(X1,mark(X2)) -> zip#(X1,X2) proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) -> zip#(mark(X1),X2) -> zip#(X1,X2) proper#(take(X1,X2)) -> proper#(X2) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(repItems(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X2) -> proper#(tail(X)) -> tail#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(tail(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X2) -> proper#(incr(X)) -> incr#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(incr(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(repItems(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X1) -> proper#(tail(X)) -> tail#(proper(X)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(tail(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X1) -> proper#(incr(X)) -> incr#(proper(X)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(incr(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) -> take#(X1,mark(X2)) -> take#(X1,X2) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) -> take#(mark(X1),X2) -> take#(X1,X2) proper#(s(X)) -> proper#(X) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(repItems(X)) -> proper#(X) proper#(s(X)) -> proper#(X) -> proper#(tail(X)) -> tail#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(tail(X)) -> proper#(X) proper#(s(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(s(X)) -> proper#(X) -> proper#(incr(X)) -> incr#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(incr(X)) -> proper#(X) proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X) proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(repItems(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(tail(X)) -> tail#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(tail(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(incr(X)) -> incr#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(incr(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(repItems(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(tail(X)) -> tail#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(tail(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(incr(X)) -> incr#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(incr(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) -> cons#(mark(X1),X2) -> cons#(X1,X2) proper#(incr(X)) -> proper#(X) -> proper#(repItems(X)) -> repItems#(proper(X)) proper#(incr(X)) -> proper#(X) -> proper#(repItems(X)) -> proper#(X) proper#(incr(X)) -> proper#(X) -> proper#(tail(X)) -> tail#(proper(X)) proper#(incr(X)) -> proper#(X) -> proper#(tail(X)) -> proper#(X) proper#(incr(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(incr(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> proper#(X1) proper#(incr(X)) -> proper#(X) -> proper#(pair(X1,X2)) -> proper#(X2) proper#(incr(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> zip#(proper(X1),proper(X2)) proper#(incr(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> proper#(X1) proper#(incr(X)) -> proper#(X) -> proper#(zip(X1,X2)) -> proper#(X2) proper#(incr(X)) -> proper#(X) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(incr(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X1) proper#(incr(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X2) proper#(incr(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(incr(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(incr(X)) -> proper#(X) -> proper#(incr(X)) -> incr#(proper(X)) proper#(incr(X)) -> proper#(X) -> proper#(incr(X)) -> proper#(X) proper#(incr(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(incr(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(incr(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(incr(X)) -> incr#(proper(X)) -> incr#(ok(X)) -> incr#(X) proper#(incr(X)) -> incr#(proper(X)) -> incr#(mark(X)) -> incr#(X) tail#(ok(X)) -> tail#(X) -> tail#(ok(X)) -> tail#(X) tail#(ok(X)) -> tail#(X) -> tail#(mark(X)) -> tail#(X) tail#(mark(X)) -> tail#(X) -> tail#(ok(X)) -> tail#(X) tail#(mark(X)) -> tail#(X) -> tail#(mark(X)) -> tail#(X) take#(ok(X1),ok(X2)) -> take#(X1,X2) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) take#(ok(X1),ok(X2)) -> take#(X1,X2) -> take#(X1,mark(X2)) -> take#(X1,X2) take#(ok(X1),ok(X2)) -> take#(X1,X2) -> take#(mark(X1),X2) -> take#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) -> take#(X1,mark(X2)) -> take#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) -> take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) -> take#(X1,mark(X2)) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) -> take#(mark(X1),X2) -> take#(X1,X2) repItems#(ok(X)) -> repItems#(X) -> repItems#(ok(X)) -> repItems#(X) repItems#(ok(X)) -> repItems#(X) -> repItems#(mark(X)) -> repItems#(X) repItems#(mark(X)) -> repItems#(X) -> repItems#(ok(X)) -> repItems#(X) repItems#(mark(X)) -> repItems#(X) -> repItems#(mark(X)) -> repItems#(X) pair#(ok(X1),ok(X2)) -> pair#(X1,X2) -> pair#(ok(X1),ok(X2)) -> pair#(X1,X2) pair#(ok(X1),ok(X2)) -> pair#(X1,X2) -> pair#(X1,mark(X2)) -> pair#(X1,X2) pair#(ok(X1),ok(X2)) -> pair#(X1,X2) -> pair#(mark(X1),X2) -> pair#(X1,X2) pair#(mark(X1),X2) -> pair#(X1,X2) -> pair#(ok(X1),ok(X2)) -> pair#(X1,X2) pair#(mark(X1),X2) -> pair#(X1,X2) -> pair#(X1,mark(X2)) -> pair#(X1,X2) pair#(mark(X1),X2) -> pair#(X1,X2) -> pair#(mark(X1),X2) -> pair#(X1,X2) pair#(X1,mark(X2)) -> pair#(X1,X2) -> pair#(ok(X1),ok(X2)) -> pair#(X1,X2) pair#(X1,mark(X2)) -> pair#(X1,X2) -> pair#(X1,mark(X2)) -> pair#(X1,X2) pair#(X1,mark(X2)) -> pair#(X1,X2) -> pair#(mark(X1),X2) -> pair#(X1,X2) zip#(ok(X1),ok(X2)) -> zip#(X1,X2) -> zip#(ok(X1),ok(X2)) -> zip#(X1,X2) zip#(ok(X1),ok(X2)) -> zip#(X1,X2) -> zip#(X1,mark(X2)) -> zip#(X1,X2) zip#(ok(X1),ok(X2)) -> zip#(X1,X2) -> zip#(mark(X1),X2) -> zip#(X1,X2) zip#(mark(X1),X2) -> zip#(X1,X2) -> zip#(ok(X1),ok(X2)) -> zip#(X1,X2) zip#(mark(X1),X2) -> zip#(X1,X2) -> zip#(X1,mark(X2)) -> zip#(X1,X2) zip#(mark(X1),X2) -> zip#(X1,X2) -> zip#(mark(X1),X2) -> zip#(X1,X2) zip#(X1,mark(X2)) -> zip#(X1,X2) -> zip#(ok(X1),ok(X2)) -> zip#(X1,X2) zip#(X1,mark(X2)) -> zip#(X1,X2) -> zip#(X1,mark(X2)) -> zip#(X1,X2) zip#(X1,mark(X2)) -> zip#(X1,X2) -> zip#(mark(X1),X2) -> zip#(X1,X2) s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X) s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(ok(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) incr#(ok(X)) -> incr#(X) -> incr#(ok(X)) -> incr#(X) incr#(ok(X)) -> incr#(X) -> incr#(mark(X)) -> incr#(X) incr#(mark(X)) -> incr#(X) -> incr#(ok(X)) -> incr#(X) incr#(mark(X)) -> incr#(X) -> incr#(mark(X)) -> incr#(X) active#(repItems(cons(X,XS))) -> repItems#(XS) -> repItems#(ok(X)) -> repItems#(X) active#(repItems(cons(X,XS))) -> repItems#(XS) -> repItems#(mark(X)) -> repItems#(X) active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(repItems(X)) -> repItems#(active(X)) -> repItems#(ok(X)) -> repItems#(X) active#(repItems(X)) -> repItems#(active(X)) -> repItems#(mark(X)) -> repItems#(X) active#(repItems(X)) -> active#(X) -> active#(repItems(X)) -> repItems#(active(X)) active#(repItems(X)) -> active#(X) -> active#(repItems(X)) -> active#(X) active#(repItems(X)) -> active#(X) -> active#(tail(X)) -> tail#(active(X)) active#(repItems(X)) -> active#(X) -> active#(tail(X)) -> active#(X) active#(repItems(X)) -> active#(X) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(repItems(X)) -> active#(X) -> active#(pair(X1,X2)) -> active#(X2) active#(repItems(X)) -> active#(X) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(repItems(X)) -> active#(X) -> active#(pair(X1,X2)) -> active#(X1) active#(repItems(X)) -> active#(X) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(repItems(X)) -> active#(X) -> active#(zip(X1,X2)) -> active#(X2) active#(repItems(X)) -> active#(X) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(repItems(X)) -> active#(X) -> active#(zip(X1,X2)) -> active#(X1) active#(repItems(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(repItems(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X2) active#(repItems(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(repItems(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X1) active#(repItems(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(repItems(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(repItems(X)) -> active#(X) -> active#(incr(X)) -> incr#(active(X)) active#(repItems(X)) -> active#(X) -> active#(incr(X)) -> active#(X) active#(repItems(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(repItems(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(repItems(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(repItems(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(repItems(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(repItems(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(repItems(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(repItems(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(repItems(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(repItems(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> s#(X) active#(repItems(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(repItems(X)) -> active#(X) -> active#(oddNs()) -> incr#(pairNs()) active#(repItems(X)) -> active#(X) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(repItems(X)) -> active#(X) -> active#(pairNs()) -> incr#(oddNs()) active#(tail(X)) -> tail#(active(X)) -> tail#(ok(X)) -> tail#(X) active#(tail(X)) -> tail#(active(X)) -> tail#(mark(X)) -> tail#(X) active#(tail(X)) -> active#(X) -> active#(repItems(X)) -> repItems#(active(X)) active#(tail(X)) -> active#(X) -> active#(repItems(X)) -> active#(X) active#(tail(X)) -> active#(X) -> active#(tail(X)) -> tail#(active(X)) active#(tail(X)) -> active#(X) -> active#(tail(X)) -> active#(X) active#(tail(X)) -> active#(X) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(tail(X)) -> active#(X) -> active#(pair(X1,X2)) -> active#(X2) active#(tail(X)) -> active#(X) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(tail(X)) -> active#(X) -> active#(pair(X1,X2)) -> active#(X1) active#(tail(X)) -> active#(X) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(tail(X)) -> active#(X) -> active#(zip(X1,X2)) -> active#(X2) active#(tail(X)) -> active#(X) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(tail(X)) -> active#(X) -> active#(zip(X1,X2)) -> active#(X1) active#(tail(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(tail(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X2) active#(tail(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(tail(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X1) active#(tail(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(tail(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(tail(X)) -> active#(X) -> active#(incr(X)) -> incr#(active(X)) active#(tail(X)) -> active#(X) -> active#(incr(X)) -> active#(X) active#(tail(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(tail(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(tail(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(tail(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(tail(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(tail(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(tail(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(tail(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(tail(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(tail(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> s#(X) active#(tail(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(tail(X)) -> active#(X) -> active#(oddNs()) -> incr#(pairNs()) active#(tail(X)) -> active#(X) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(tail(X)) -> active#(X) -> active#(pairNs()) -> incr#(oddNs()) active#(pair(X1,X2)) -> pair#(active(X1),X2) -> pair#(ok(X1),ok(X2)) -> pair#(X1,X2) active#(pair(X1,X2)) -> pair#(active(X1),X2) -> pair#(X1,mark(X2)) -> pair#(X1,X2) active#(pair(X1,X2)) -> pair#(active(X1),X2) -> pair#(mark(X1),X2) -> pair#(X1,X2) active#(pair(X1,X2)) -> pair#(X1,active(X2)) -> pair#(ok(X1),ok(X2)) -> pair#(X1,X2) active#(pair(X1,X2)) -> pair#(X1,active(X2)) -> pair#(X1,mark(X2)) -> pair#(X1,X2) active#(pair(X1,X2)) -> pair#(X1,active(X2)) -> pair#(mark(X1),X2) -> pair#(X1,X2) active#(pair(X1,X2)) -> active#(X2) -> active#(repItems(X)) -> repItems#(active(X)) active#(pair(X1,X2)) -> active#(X2) -> active#(repItems(X)) -> active#(X) active#(pair(X1,X2)) -> active#(X2) -> active#(tail(X)) -> tail#(active(X)) active#(pair(X1,X2)) -> active#(X2) -> active#(tail(X)) -> active#(X) active#(pair(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(pair(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(pair(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(pair(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(pair(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(pair(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(pair(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(pair(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(pair(X1,X2)) -> active#(X2) -> active#(incr(X)) -> incr#(active(X)) active#(pair(X1,X2)) -> active#(X2) -> active#(incr(X)) -> active#(X) active#(pair(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(pair(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X2) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(pair(X1,X2)) -> active#(X2) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(pair(X1,X2)) -> active#(X2) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(pair(X1,X2)) -> active#(X2) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(pair(X1,X2)) -> active#(X2) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(pair(X1,X2)) -> active#(X2) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(pair(X1,X2)) -> active#(X2) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(pair(X1,X2)) -> active#(X2) -> active#(incr(cons(X,XS))) -> s#(X) active#(pair(X1,X2)) -> active#(X2) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(pair(X1,X2)) -> active#(X2) -> active#(oddNs()) -> incr#(pairNs()) active#(pair(X1,X2)) -> active#(X2) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(pair(X1,X2)) -> active#(X2) -> active#(pairNs()) -> incr#(oddNs()) active#(pair(X1,X2)) -> active#(X1) -> active#(repItems(X)) -> repItems#(active(X)) active#(pair(X1,X2)) -> active#(X1) -> active#(repItems(X)) -> active#(X) active#(pair(X1,X2)) -> active#(X1) -> active#(tail(X)) -> tail#(active(X)) active#(pair(X1,X2)) -> active#(X1) -> active#(tail(X)) -> active#(X) active#(pair(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(pair(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(pair(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(pair(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(pair(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(pair(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(pair(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(pair(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(pair(X1,X2)) -> active#(X1) -> active#(incr(X)) -> incr#(active(X)) active#(pair(X1,X2)) -> active#(X1) -> active#(incr(X)) -> active#(X) active#(pair(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(pair(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(pair(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(pair(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(pair(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(pair(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(pair(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(pair(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(pair(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> s#(X) active#(pair(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(pair(X1,X2)) -> active#(X1) -> active#(oddNs()) -> incr#(pairNs()) active#(pair(X1,X2)) -> active#(X1) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(pair(X1,X2)) -> active#(X1) -> active#(pairNs()) -> incr#(oddNs()) active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) -> pair#(ok(X1),ok(X2)) -> pair#(X1,X2) active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) -> pair#(X1,mark(X2)) -> pair#(X1,X2) active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) -> pair#(mark(X1),X2) -> pair#(X1,X2) active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) -> zip#(ok(X1),ok(X2)) -> zip#(X1,X2) active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) -> zip#(X1,mark(X2)) -> zip#(X1,X2) active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) -> zip#(mark(X1),X2) -> zip#(X1,X2) active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(zip(X1,X2)) -> zip#(active(X1),X2) -> zip#(ok(X1),ok(X2)) -> zip#(X1,X2) active#(zip(X1,X2)) -> zip#(active(X1),X2) -> zip#(X1,mark(X2)) -> zip#(X1,X2) active#(zip(X1,X2)) -> zip#(active(X1),X2) -> zip#(mark(X1),X2) -> zip#(X1,X2) active#(zip(X1,X2)) -> zip#(X1,active(X2)) -> zip#(ok(X1),ok(X2)) -> zip#(X1,X2) active#(zip(X1,X2)) -> zip#(X1,active(X2)) -> zip#(X1,mark(X2)) -> zip#(X1,X2) active#(zip(X1,X2)) -> zip#(X1,active(X2)) -> zip#(mark(X1),X2) -> zip#(X1,X2) active#(zip(X1,X2)) -> active#(X2) -> active#(repItems(X)) -> repItems#(active(X)) active#(zip(X1,X2)) -> active#(X2) -> active#(repItems(X)) -> active#(X) active#(zip(X1,X2)) -> active#(X2) -> active#(tail(X)) -> tail#(active(X)) active#(zip(X1,X2)) -> active#(X2) -> active#(tail(X)) -> active#(X) active#(zip(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(zip(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> active#(X2) active#(zip(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(zip(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(zip(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> active#(X2) active#(zip(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(zip(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(zip(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> active#(X2) active#(zip(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(zip(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(zip(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(zip(X1,X2)) -> active#(X2) -> active#(incr(X)) -> incr#(active(X)) active#(zip(X1,X2)) -> active#(X2) -> active#(incr(X)) -> active#(X) active#(zip(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(zip(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> active#(X2) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(zip(X1,X2)) -> active#(X2) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(zip(X1,X2)) -> active#(X2) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(zip(X1,X2)) -> active#(X2) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(zip(X1,X2)) -> active#(X2) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(zip(X1,X2)) -> active#(X2) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(zip(X1,X2)) -> active#(X2) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(zip(X1,X2)) -> active#(X2) -> active#(incr(cons(X,XS))) -> s#(X) active#(zip(X1,X2)) -> active#(X2) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(zip(X1,X2)) -> active#(X2) -> active#(oddNs()) -> incr#(pairNs()) active#(zip(X1,X2)) -> active#(X2) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(zip(X1,X2)) -> active#(X2) -> active#(pairNs()) -> incr#(oddNs()) active#(zip(X1,X2)) -> active#(X1) -> active#(repItems(X)) -> repItems#(active(X)) active#(zip(X1,X2)) -> active#(X1) -> active#(repItems(X)) -> active#(X) active#(zip(X1,X2)) -> active#(X1) -> active#(tail(X)) -> tail#(active(X)) active#(zip(X1,X2)) -> active#(X1) -> active#(tail(X)) -> active#(X) active#(zip(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(zip(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> active#(X2) active#(zip(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(zip(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(zip(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> active#(X2) active#(zip(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(zip(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(zip(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X2) active#(zip(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(zip(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(zip(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(zip(X1,X2)) -> active#(X1) -> active#(incr(X)) -> incr#(active(X)) active#(zip(X1,X2)) -> active#(X1) -> active#(incr(X)) -> active#(X) active#(zip(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(zip(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(zip(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(zip(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(zip(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(zip(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(zip(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(zip(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(zip(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> s#(X) active#(zip(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(zip(X1,X2)) -> active#(X1) -> active#(oddNs()) -> incr#(pairNs()) active#(zip(X1,X2)) -> active#(X1) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(zip(X1,X2)) -> active#(X1) -> active#(pairNs()) -> incr#(oddNs()) active#(take(X1,X2)) -> take#(active(X1),X2) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) active#(take(X1,X2)) -> take#(active(X1),X2) -> take#(X1,mark(X2)) -> take#(X1,X2) active#(take(X1,X2)) -> take#(active(X1),X2) -> take#(mark(X1),X2) -> take#(X1,X2) active#(take(X1,X2)) -> take#(X1,active(X2)) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) active#(take(X1,X2)) -> take#(X1,active(X2)) -> take#(X1,mark(X2)) -> take#(X1,X2) active#(take(X1,X2)) -> take#(X1,active(X2)) -> take#(mark(X1),X2) -> take#(X1,X2) active#(take(X1,X2)) -> active#(X2) -> active#(repItems(X)) -> repItems#(active(X)) active#(take(X1,X2)) -> active#(X2) -> active#(repItems(X)) -> active#(X) active#(take(X1,X2)) -> active#(X2) -> active#(tail(X)) -> tail#(active(X)) active#(take(X1,X2)) -> active#(X2) -> active#(tail(X)) -> active#(X) active#(take(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(take(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) -> active#(pair(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(take(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) -> active#(zip(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(take(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(take(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(take(X1,X2)) -> active#(X2) -> active#(incr(X)) -> incr#(active(X)) active#(take(X1,X2)) -> active#(X2) -> active#(incr(X)) -> active#(X) active#(take(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X2) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(take(X1,X2)) -> active#(X2) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(take(X1,X2)) -> active#(X2) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(take(X1,X2)) -> active#(X2) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(take(X1,X2)) -> active#(X2) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(take(X1,X2)) -> active#(X2) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(take(X1,X2)) -> active#(X2) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(take(X1,X2)) -> active#(X2) -> active#(incr(cons(X,XS))) -> s#(X) active#(take(X1,X2)) -> active#(X2) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(take(X1,X2)) -> active#(X2) -> active#(oddNs()) -> incr#(pairNs()) active#(take(X1,X2)) -> active#(X2) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(take(X1,X2)) -> active#(X2) -> active#(pairNs()) -> incr#(oddNs()) active#(take(X1,X2)) -> active#(X1) -> active#(repItems(X)) -> repItems#(active(X)) active#(take(X1,X2)) -> active#(X1) -> active#(repItems(X)) -> active#(X) active#(take(X1,X2)) -> active#(X1) -> active#(tail(X)) -> tail#(active(X)) active#(take(X1,X2)) -> active#(X1) -> active#(tail(X)) -> active#(X) active#(take(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(take(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(take(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(take(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(take(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(take(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(take(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(take(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(take(X1,X2)) -> active#(X1) -> active#(incr(X)) -> incr#(active(X)) active#(take(X1,X2)) -> active#(X1) -> active#(incr(X)) -> active#(X) active#(take(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(take(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(take(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(take(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(take(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(take(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(take(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(take(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(take(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> s#(X) active#(take(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(take(X1,X2)) -> active#(X1) -> active#(oddNs()) -> incr#(pairNs()) active#(take(X1,X2)) -> active#(X1) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(take(X1,X2)) -> active#(X1) -> active#(pairNs()) -> incr#(oddNs()) active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X) active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X) active#(s(X)) -> active#(X) -> active#(repItems(X)) -> repItems#(active(X)) active#(s(X)) -> active#(X) -> active#(repItems(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(tail(X)) -> tail#(active(X)) active#(s(X)) -> active#(X) -> active#(tail(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(pair(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(pair(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(zip(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(zip(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(incr(X)) -> incr#(active(X)) active#(s(X)) -> active#(X) -> active#(incr(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(s(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(s(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(s(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(s(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(s(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(s(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(s(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> s#(X) active#(s(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(s(X)) -> active#(X) -> active#(oddNs()) -> incr#(pairNs()) active#(s(X)) -> active#(X) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(s(X)) -> active#(X) -> active#(pairNs()) -> incr#(oddNs()) active#(cons(X1,X2)) -> cons#(active(X1),X2) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(cons(X1,X2)) -> cons#(active(X1),X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(cons(X1,X2)) -> active#(X1) -> active#(repItems(X)) -> repItems#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(repItems(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(tail(X)) -> tail#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(tail(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(cons(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(pair(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(cons(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(zip(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(cons(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(incr(X)) -> incr#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(incr(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(cons(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(cons(X1,X2)) -> active#(X1) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(cons(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(cons(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(cons(X1,X2)) -> active#(X1) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(cons(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(cons(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> s#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(cons(X1,X2)) -> active#(X1) -> active#(oddNs()) -> incr#(pairNs()) active#(cons(X1,X2)) -> active#(X1) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(cons(X1,X2)) -> active#(X1) -> active#(pairNs()) -> incr#(oddNs()) active#(incr(cons(X,XS))) -> s#(X) -> s#(ok(X)) -> s#(X) active#(incr(cons(X,XS))) -> s#(X) -> s#(mark(X)) -> s#(X) active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(incr(cons(X,XS))) -> incr#(XS) -> incr#(ok(X)) -> incr#(X) active#(incr(cons(X,XS))) -> incr#(XS) -> incr#(mark(X)) -> incr#(X) active#(incr(X)) -> incr#(active(X)) -> incr#(ok(X)) -> incr#(X) active#(incr(X)) -> incr#(active(X)) -> incr#(mark(X)) -> incr#(X) active#(incr(X)) -> active#(X) -> active#(repItems(X)) -> repItems#(active(X)) active#(incr(X)) -> active#(X) -> active#(repItems(X)) -> active#(X) active#(incr(X)) -> active#(X) -> active#(tail(X)) -> tail#(active(X)) active#(incr(X)) -> active#(X) -> active#(tail(X)) -> active#(X) active#(incr(X)) -> active#(X) -> active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(incr(X)) -> active#(X) -> active#(pair(X1,X2)) -> active#(X2) active#(incr(X)) -> active#(X) -> active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(incr(X)) -> active#(X) -> active#(pair(X1,X2)) -> active#(X1) active#(incr(X)) -> active#(X) -> active#(zip(X1,X2)) -> zip#(X1,active(X2)) active#(incr(X)) -> active#(X) -> active#(zip(X1,X2)) -> active#(X2) active#(incr(X)) -> active#(X) -> active#(zip(X1,X2)) -> zip#(active(X1),X2) active#(incr(X)) -> active#(X) -> active#(zip(X1,X2)) -> active#(X1) active#(incr(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(incr(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X2) active#(incr(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(incr(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X1) active#(incr(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(incr(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(incr(X)) -> active#(X) -> active#(incr(X)) -> incr#(active(X)) active#(incr(X)) -> active#(X) -> active#(incr(X)) -> active#(X) active#(incr(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(incr(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(incr(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> cons#(X,cons(X,repItems(XS))) active#(incr(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> cons#(X,repItems(XS)) active#(incr(X)) -> active#(X) -> active#(repItems(cons(X,XS))) -> repItems#(XS) active#(incr(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> cons#(pair(X,Y),zip(XS,YS)) active#(incr(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> pair#(X,Y) active#(incr(X)) -> active#(X) -> active#(zip(cons(X,XS),cons(Y,YS))) -> zip#(XS,YS) active#(incr(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> cons#(s(X),incr(XS)) active#(incr(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> s#(X) active#(incr(X)) -> active#(X) -> active#(incr(cons(X,XS))) -> incr#(XS) active#(incr(X)) -> active#(X) -> active#(oddNs()) -> incr#(pairNs()) active#(incr(X)) -> active#(X) -> active#(pairNs()) -> cons#(0(),incr(oddNs())) active#(incr(X)) -> active#(X) -> active#(pairNs()) -> incr#(oddNs()) active#(oddNs()) -> incr#(pairNs()) -> incr#(ok(X)) -> incr#(X) active#(oddNs()) -> incr#(pairNs()) -> incr#(mark(X)) -> incr#(X) active#(pairNs()) -> cons#(0(),incr(oddNs())) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(pairNs()) -> cons#(0(),incr(oddNs())) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(pairNs()) -> incr#(oddNs()) -> incr#(ok(X)) -> incr#(X) active#(pairNs()) -> incr#(oddNs()) -> incr#(mark(X)) -> incr#(X) SCC Processor: #sccs: 11 #rules: 44 #arcs: 796/5929 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Usable Rule Processor: DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) incr(mark(X)) -> mark(incr(X)) incr(ok(X)) -> ok(incr(X)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) repItems(mark(X)) -> mark(repItems(X)) repItems(ok(X)) -> ok(repItems(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) LPO Processor: argument filtering: pi(pairNs) = [] pi(active) = 0 pi(0) = [] pi(oddNs) = [] pi(incr) = [0] pi(cons) = 0 pi(mark) = [0] pi(s) = 0 pi(take) = [0,1] pi(nil) = [] pi(zip) = [0,1] pi(pair) = [0,1] pi(tail) = 0 pi(repItems) = [0] pi(proper) = 0 pi(ok) = 0 pi(top#) = 0 usable rules: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) incr(mark(X)) -> mark(incr(X)) incr(ok(X)) -> ok(incr(X)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) repItems(mark(X)) -> mark(repItems(X)) repItems(ok(X)) -> ok(repItems(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) precedence: oddNs > zip > pair > repItems ~ incr > take ~ pairNs > top# ~ ok ~ proper ~ tail ~ nil ~ s ~ mark ~ cons ~ 0 ~ active problem: DPs: top#(ok(X)) -> top#(active(X)) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) incr(mark(X)) -> mark(incr(X)) incr(ok(X)) -> ok(incr(X)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) repItems(mark(X)) -> mark(repItems(X)) repItems(ok(X)) -> ok(repItems(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) Restore Modifier: DPs: top#(ok(X)) -> top#(active(X)) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Usable Rule Processor: DPs: top#(ok(X)) -> top#(active(X)) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) incr(mark(X)) -> mark(incr(X)) incr(ok(X)) -> ok(incr(X)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) repItems(mark(X)) -> mark(repItems(X)) repItems(ok(X)) -> ok(repItems(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) KBO Processor: argument filtering: pi(pairNs) = [] pi(active) = 0 pi(0) = [] pi(oddNs) = [] pi(incr) = 0 pi(cons) = [0] pi(mark) = [] pi(s) = [0] pi(take) = [0,1] pi(zip) = [0,1] pi(pair) = [0] pi(tail) = 0 pi(repItems) = 0 pi(ok) = [0] pi(top#) = 0 usable rules: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) incr(mark(X)) -> mark(incr(X)) incr(ok(X)) -> ok(incr(X)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) repItems(mark(X)) -> mark(repItems(X)) repItems(ok(X)) -> ok(repItems(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) weight function: w0 = 1 w(top#) = w(ok) = w(repItems) = w(pair) = w(s) = w(mark) = w( cons) = w(oddNs) = w(0) = w(pairNs) = 1 w(tail) = w(zip) = w(take) = w(incr) = w(active) = 0 precedence: pair > s ~ cons ~ oddNs ~ pairNs > top# ~ ok ~ repItems ~ tail ~ zip ~ take ~ mark ~ incr ~ 0 ~ active problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) incr(mark(X)) -> mark(incr(X)) incr(ok(X)) -> ok(incr(X)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) repItems(mark(X)) -> mark(repItems(X)) repItems(ok(X)) -> ok(repItems(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) tail(mark(X)) -> mark(tail(X)) tail(ok(X)) -> ok(tail(X)) Qed DPs: active#(cons(X1,X2)) -> active#(X1) active#(incr(X)) -> active#(X) active#(s(X)) -> active#(X) active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X2) active#(zip(X1,X2)) -> active#(X1) active#(zip(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X2) active#(tail(X)) -> active#(X) active#(repItems(X)) -> active#(X) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(active#) = 0 problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(incr(X)) -> proper#(X) proper#(s(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) proper#(zip(X1,X2)) -> proper#(X2) proper#(zip(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X1) proper#(tail(X)) -> proper#(X) proper#(repItems(X)) -> proper#(X) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(proper#) = 0 problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: repItems#(mark(X)) -> repItems#(X) repItems#(ok(X)) -> repItems#(X) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(repItems#) = 0 problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: tail#(mark(X)) -> tail#(X) tail#(ok(X)) -> tail#(X) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(tail#) = 0 problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: pair#(mark(X1),X2) -> pair#(X1,X2) pair#(X1,mark(X2)) -> pair#(X1,X2) pair#(ok(X1),ok(X2)) -> pair#(X1,X2) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(pair#) = 0 problem: DPs: pair#(X1,mark(X2)) -> pair#(X1,X2) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(pair#) = 1 problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: zip#(mark(X1),X2) -> zip#(X1,X2) zip#(X1,mark(X2)) -> zip#(X1,X2) zip#(ok(X1),ok(X2)) -> zip#(X1,X2) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(zip#) = 0 problem: DPs: zip#(X1,mark(X2)) -> zip#(X1,X2) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(zip#) = 1 problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(ok(X1),ok(X2)) -> take#(X1,X2) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(take#) = 0 problem: DPs: take#(X1,mark(X2)) -> take#(X1,X2) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(take#) = 1 problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: s#(mark(X)) -> s#(X) s#(ok(X)) -> s#(X) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: incr#(mark(X)) -> incr#(X) incr#(ok(X)) -> incr#(X) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(incr#) = 0 problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: TRS: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) active(cons(X1,X2)) -> cons(active(X1),X2) active(incr(X)) -> incr(active(X)) active(s(X)) -> s(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(zip(X1,X2)) -> zip(active(X1),X2) active(zip(X1,X2)) -> zip(X1,active(X2)) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(tail(X)) -> tail(active(X)) active(repItems(X)) -> repItems(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) incr(mark(X)) -> mark(incr(X)) s(mark(X)) -> mark(s(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) zip(mark(X1),X2) -> mark(zip(X1,X2)) zip(X1,mark(X2)) -> mark(zip(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) tail(mark(X)) -> mark(tail(X)) repItems(mark(X)) -> mark(repItems(X)) proper(pairNs()) -> ok(pairNs()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(incr(X)) -> incr(proper(X)) proper(oddNs()) -> ok(oddNs()) proper(s(X)) -> s(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(tail(X)) -> tail(proper(X)) proper(repItems(X)) -> repItems(proper(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) incr(ok(X)) -> ok(incr(X)) s(ok(X)) -> ok(s(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) tail(ok(X)) -> ok(tail(X)) repItems(ok(X)) -> ok(repItems(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed