- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__zeros -> cons(0,zeros) [2] a__and(tt,X) -> mark(X) [3] a__length(nil) -> 0 [4] a__length(cons(N,L)) -> s(a__length(mark(L))) [5] a__take(0,IL) -> nil [6] a__take(s(M),cons(N,IL)) -> cons(mark(N),take(M,IL)) [7] mark(zeros) -> a__zeros [8] mark(and(X1,X2)) -> a__and(mark(X1),X2) [9] mark(length(X)) -> a__length(mark(X)) [10] mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) [11] mark(cons(X1,X2)) -> cons(mark(X1),X2) [12] mark(0) -> 0 [13] mark(tt) -> tt [14] mark(nil) -> nil [15] mark(s(X)) -> s(mark(X)) [16] a__zeros -> zeros [17] a__and(X1,X2) -> and(X1,X2) [18] a__length(X) -> length(X) [19] a__take(X1,X2) -> take(X1,X2) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(tt) >= tt ; mark(nil) >= nil ; mark(s(X)) >= s(mark(X)) ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(length(X)) >= a__length(mark(X)) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__length(cons(N,L)) >= s(a__length(mark(L))) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; a__take(0,IL) >= nil ; a__take(s(M),cons(N,IL)) >= cons(mark(N),take(M,IL)) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__take(s(M),cons(N,IL)) >= Marked_mark(N) ; Marked_a__length(cons(N,L)) >= Marked_a__length(mark(L)) ; Marked_a__length(cons(N,L)) >= Marked_mark(L) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(take(X1,X2)) >= Marked_a__take(mark(X1),mark(X2)) ; Marked_mark(take(X1,X2)) >= Marked_mark(X1) ; Marked_mark(take(X1,X2)) >= Marked_mark(X2) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(length(X)) >= Marked_a__length(mark(X)) ; Marked_mark(length(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__take(s(M),cons(N,IL)) > Marked_mark(N) ; } { Marked_a__length(cons(N,L)) > Marked_a__length(mark(L)) ; } { Marked_a__length(cons(N,L)) > Marked_mark(L) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(take(X1,X2)) > Marked_a__take(mark(X1),mark(X2)) ; } { Marked_mark(take(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(take(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(length(X)) > Marked_a__length(mark(X)) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__zeros >= cons(0,zeros) constraint: a__zeros >= zeros constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(tt) >= tt constraint: mark(nil) >= nil constraint: mark(s(X)) >= s(mark(X)) constraint: mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: mark(length(X)) >= a__length(mark(X)) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__length(cons(N,L)) >= s(a__length(mark(L))) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: a__take(0,IL) >= nil constraint: a__take(s(M),cons(N,IL)) >= cons(mark(N),take(M,IL)) constraint: a__take(X1,X2) >= take(X1,X2) constraint: Marked_a__take(s(M),cons(N,IL)) >= Marked_mark(N) constraint: Marked_a__length(cons(N,L)) >= Marked_a__length(mark(L)) constraint: Marked_a__length(cons(N,L)) >= Marked_mark(L) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(take(X1,X2)) >= Marked_a__take(mark(X1),mark(X2)) constraint: Marked_mark(take(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(take(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(length(X)) >= Marked_a__length(mark(X)) constraint: Marked_mark(length(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(tt) >= tt ; mark(nil) >= nil ; mark(s(X)) >= s(mark(X)) ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(length(X)) >= a__length(mark(X)) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__length(cons(N,L)) >= s(a__length(mark(L))) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; a__take(0,IL) >= nil ; a__take(s(M),cons(N,IL)) >= cons(mark(N),take(M,IL)) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__take(s(M),cons(N,IL)) >= Marked_mark(N) ; Marked_a__length(cons(N,L)) >= Marked_a__length(mark(L)) ; Marked_a__length(cons(N,L)) >= Marked_mark(L) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(take(X1,X2)) >= Marked_a__take(mark(X1),mark(X2)) ; Marked_mark(take(X1,X2)) >= Marked_mark(X1) ; Marked_mark(take(X1,X2)) >= Marked_mark(X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(length(X)) >= Marked_a__length(mark(X)) ; Marked_mark(length(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__take(s(M),cons(N,IL)) > Marked_mark(N) ; } { Marked_a__length(cons(N,L)) > Marked_a__length(mark(L)) ; } { Marked_a__length(cons(N,L)) > Marked_mark(L) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(take(X1,X2)) > Marked_a__take(mark(X1),mark(X2)) ; } { Marked_mark(take(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(take(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(length(X)) > Marked_a__length(mark(X)) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__zeros >= cons(0,zeros) constraint: a__zeros >= zeros constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(tt) >= tt constraint: mark(nil) >= nil constraint: mark(s(X)) >= s(mark(X)) constraint: mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: mark(length(X)) >= a__length(mark(X)) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__length(cons(N,L)) >= s(a__length(mark(L))) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: a__take(0,IL) >= nil constraint: a__take(s(M),cons(N,IL)) >= cons(mark(N),take(M,IL)) constraint: a__take(X1,X2) >= take(X1,X2) constraint: Marked_a__take(s(M),cons(N,IL)) >= Marked_mark(N) constraint: Marked_a__length(cons(N,L)) >= Marked_a__length(mark(L)) constraint: Marked_a__length(cons(N,L)) >= Marked_mark(L) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(take(X1,X2)) >= Marked_a__take(mark(X1),mark(X2)) constraint: Marked_mark(take(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(take(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(length(X)) >= Marked_a__length(mark(X)) constraint: Marked_mark(length(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(tt) >= tt ; mark(nil) >= nil ; mark(s(X)) >= s(mark(X)) ; mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(length(X)) >= a__length(mark(X)) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__length(cons(N,L)) >= s(a__length(mark(L))) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; a__take(0,IL) >= nil ; a__take(s(M),cons(N,IL)) >= cons(mark(N),take(M,IL)) ; a__take(X1,X2) >= take(X1,X2) ; Marked_a__length(cons(N,L)) >= Marked_a__length(mark(L)) ; Marked_a__length(cons(N,L)) >= Marked_mark(L) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(length(X)) >= Marked_a__length(mark(X)) ; Marked_mark(length(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__length(cons(N,L)) > Marked_a__length(mark(L)) ; } { Marked_a__length(cons(N,L)) > Marked_mark(L) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(length(X)) > Marked_a__length(mark(X)) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__zeros >= cons(0,zeros) constraint: a__zeros >= zeros constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(tt) >= tt constraint: mark(nil) >= nil constraint: mark(s(X)) >= s(mark(X)) constraint: mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: mark(length(X)) >= a__length(mark(X)) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__length(cons(N,L)) >= s(a__length(mark(L))) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: a__take(0,IL) >= nil constraint: a__take(s(M),cons(N,IL)) >= cons(mark(N),take(M,IL)) constraint: a__take(X1,X2) >= take(X1,X2) constraint: Marked_a__length(cons(N,L)) >= Marked_a__length(mark(L)) constraint: Marked_a__length(cons(N,L)) >= Marked_mark(L) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(length(X)) >= Marked_a__length(mark(X)) constraint: Marked_mark(length(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> --> --> --> --> --> -->