/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: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) Proof: DP Processor: DPs: a__from#(X) -> mark#(X) a__after#(0(),XS) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) TDG Processor: DPs: a__from#(X) -> mark#(X) a__after#(0(),XS) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) graph: a__after#(0(),XS) -> mark#(XS) -> mark#(s(X)) -> mark#(X) a__after#(0(),XS) -> mark#(XS) -> mark#(cons(X1,X2)) -> mark#(X1) a__after#(0(),XS) -> mark#(XS) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) a__after#(0(),XS) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X1) a__after#(0(),XS) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X2) a__after#(0(),XS) -> mark#(XS) -> mark#(from(X)) -> a__from#(mark(X)) a__after#(0(),XS) -> mark#(XS) -> mark#(from(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) -> a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) -> a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) -> a__after#(s(N),cons(X,XS)) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) -> a__after#(0(),XS) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(cons(X1,X2)) -> mark#(X1) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(after(X1,X2)) -> mark#(X1) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(after(X1,X2)) -> mark#(X2) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(from(X)) -> a__from#(mark(X)) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(from(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(s(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(cons(X1,X2)) -> mark#(X1) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X1) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X2) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(from(X)) -> a__from#(mark(X)) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(from(X)) -> mark#(X) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) -> a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) -> a__after#(s(N),cons(X,XS)) -> mark#(N) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) -> a__after#(s(N),cons(X,XS)) -> mark#(XS) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) -> a__after#(0(),XS) -> mark#(XS) mark#(after(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> a__from#(mark(X)) mark#(after(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(mark(X)) mark#(after(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) -> a__from#(X) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) a__from#(X) -> mark#(X) -> mark#(s(X)) -> mark#(X) a__from#(X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) a__from#(X) -> mark#(X) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) a__from#(X) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X1) a__from#(X) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X2) a__from#(X) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) a__from#(X) -> mark#(X) -> mark#(from(X)) -> mark#(X) Arctic Interpretation Processor: dimension: 1 usable rules: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) interpretation: [a__after#](x0, x1) = x0 + x1 + 0, [mark#](x0) = x0 + -16, [a__from#](x0) = x0 + 0, [after](x0, x1) = x0 + x1 + 0, [a__after](x0, x1) = x0 + x1 + 0, [0] = 0, [cons](x0, x1) = x0 + x1 + 1, [from](x0) = 1x0 + 1, [s](x0) = x0 + 0, [mark](x0) = x0 + 0, [a__from](x0) = 1x0 + 1 orientation: a__from#(X) = X + 0 >= X + -16 = mark#(X) a__after#(0(),XS) = XS + 0 >= XS + -16 = mark#(XS) a__after#(s(N),cons(X,XS)) = N + X + XS + 1 >= XS + -16 = mark#(XS) a__after#(s(N),cons(X,XS)) = N + X + XS + 1 >= N + -16 = mark#(N) a__after#(s(N),cons(X,XS)) = N + X + XS + 1 >= N + XS + 0 = a__after#(mark(N),mark(XS)) mark#(from(X)) = 1X + 1 >= X + -16 = mark#(X) mark#(from(X)) = 1X + 1 >= X + 0 = a__from#(mark(X)) mark#(after(X1,X2)) = X1 + X2 + 0 >= X2 + -16 = mark#(X2) mark#(after(X1,X2)) = X1 + X2 + 0 >= X1 + -16 = mark#(X1) mark#(after(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a__after#(mark(X1),mark(X2)) mark#(cons(X1,X2)) = X1 + X2 + 1 >= X1 + -16 = mark#(X1) mark#(s(X)) = X + 0 >= X + -16 = mark#(X) a__from(X) = 1X + 1 >= 1X + 1 = cons(mark(X),from(s(X))) a__after(0(),XS) = XS + 0 >= XS + 0 = mark(XS) a__after(s(N),cons(X,XS)) = N + X + XS + 1 >= N + XS + 0 = a__after(mark(N),mark(XS)) mark(from(X)) = 1X + 1 >= 1X + 1 = a__from(mark(X)) mark(after(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(mark(X1),X2) mark(s(X)) = X + 0 >= X + 0 = s(mark(X)) mark(0()) = 0 >= 0 = 0() a__from(X) = 1X + 1 >= 1X + 1 = from(X) a__after(X1,X2) = X1 + X2 + 0 >= X1 + X2 + 0 = after(X1,X2) problem: DPs: a__from#(X) -> mark#(X) a__after#(0(),XS) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) Restore Modifier: DPs: a__from#(X) -> mark#(X) a__after#(0(),XS) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) SCC Processor: #sccs: 1 #rules: 9 #arcs: 72/100 DPs: a__after#(0(),XS) -> mark#(XS) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) a__after#(s(N),cons(X,XS)) -> mark#(XS) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) Arctic Interpretation Processor: dimension: 1 usable rules: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) interpretation: [a__after#](x0, x1) = x0 + 4x1, [mark#](x0) = x0 + 0, [after](x0, x1) = 7x0 + 6x1 + 0, [a__after](x0, x1) = 7x0 + 6x1 + 0, [0] = 0, [cons](x0, x1) = x0 + x1 + 0, [from](x0) = 5x0 + 5, [s](x0) = x0 + 0, [mark](x0) = x0, [a__from](x0) = 5x0 + 5 orientation: a__after#(0(),XS) = 4XS + 0 >= XS + 0 = mark#(XS) mark#(after(X1,X2)) = 7X1 + 6X2 + 0 >= X2 + 0 = mark#(X2) mark#(after(X1,X2)) = 7X1 + 6X2 + 0 >= X1 + 0 = mark#(X1) mark#(after(X1,X2)) = 7X1 + 6X2 + 0 >= X1 + 4X2 = a__after#(mark(X1),mark(X2)) a__after#(s(N),cons(X,XS)) = N + 4X + 4XS + 4 >= XS + 0 = mark#(XS) mark#(cons(X1,X2)) = X1 + X2 + 0 >= X1 + 0 = mark#(X1) mark#(s(X)) = X + 0 >= X + 0 = mark#(X) a__after#(s(N),cons(X,XS)) = N + 4X + 4XS + 4 >= N + 0 = mark#(N) a__after#(s(N),cons(X,XS)) = N + 4X + 4XS + 4 >= N + 4XS = a__after#(mark(N),mark(XS)) a__from(X) = 5X + 5 >= 5X + 5 = cons(mark(X),from(s(X))) a__after(0(),XS) = 6XS + 7 >= XS = mark(XS) a__after(s(N),cons(X,XS)) = 7N + 6X + 6XS + 7 >= 7N + 6XS + 0 = a__after(mark(N),mark(XS)) mark(from(X)) = 5X + 5 >= 5X + 5 = a__from(mark(X)) mark(after(X1,X2)) = 7X1 + 6X2 + 0 >= 7X1 + 6X2 + 0 = a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(mark(X1),X2) mark(s(X)) = X + 0 >= X + 0 = s(mark(X)) mark(0()) = 0 >= 0 = 0() a__from(X) = 5X + 5 >= 5X + 5 = from(X) a__after(X1,X2) = 7X1 + 6X2 + 0 >= 7X1 + 6X2 + 0 = after(X1,X2) problem: DPs: a__after#(0(),XS) -> mark#(XS) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) Restore Modifier: DPs: a__after#(0(),XS) -> mark#(XS) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) SCC Processor: #sccs: 2 #rules: 5 #arcs: 43/49 DPs: a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) Arctic Interpretation Processor: dimension: 1 usable rules: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) interpretation: [a__after#](x0, x1) = x0, [after](x0, x1) = 1x1, [a__after](x0, x1) = 1x1, [0] = 0, [cons](x0, x1) = x1, [from](x0) = 0, [s](x0) = 1x0, [mark](x0) = x0, [a__from](x0) = 0 orientation: a__after#(s(N),cons(X,XS)) = 1N >= N = a__after#(mark(N),mark(XS)) a__from(X) = 0 >= 0 = cons(mark(X),from(s(X))) a__after(0(),XS) = 1XS >= XS = mark(XS) a__after(s(N),cons(X,XS)) = 1XS >= 1XS = a__after(mark(N),mark(XS)) mark(from(X)) = 0 >= 0 = a__from(mark(X)) mark(after(X1,X2)) = 1X2 >= 1X2 = a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) = X2 >= X2 = cons(mark(X1),X2) mark(s(X)) = 1X >= 1X = s(mark(X)) mark(0()) = 0 >= 0 = 0() a__from(X) = 0 >= 0 = from(X) a__after(X1,X2) = 1X2 >= 1X2 = after(X1,X2) problem: DPs: TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) Qed DPs: mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) Size-Change Termination Processor: DPs: TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) The DP: mark#(after(X1,X2)) -> mark#(X2) has the edges: 0 > 0 The DP: mark#(after(X1,X2)) -> mark#(X1) has the edges: 0 > 0 The DP: mark#(cons(X1,X2)) -> mark#(X1) has the edges: 0 > 0 The DP: mark#(s(X)) -> mark#(X) has the edges: 0 > 0 Qed