- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(zeros) -> mark(cons(0,zeros)) [2] active(and(tt,X)) -> mark(X) [3] active(length(nil)) -> mark(0) [4] active(length(cons(N,L))) -> mark(s(length(L))) [5] mark(zeros) -> active(zeros) [6] mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) [7] mark(0) -> active(0) [8] mark(and(X1,X2)) -> active(and(mark(X1),X2)) [9] mark(tt) -> active(tt) [10] mark(length(X)) -> active(length(mark(X))) [11] mark(nil) -> active(nil) [12] mark(s(X)) -> active(s(mark(X))) [13] cons(mark(X1),X2) -> cons(X1,X2) [14] cons(X1,mark(X2)) -> cons(X1,X2) [15] cons(active(X1),X2) -> cons(X1,X2) [16] cons(X1,active(X2)) -> cons(X1,X2) [17] and(mark(X1),X2) -> and(X1,X2) [18] and(X1,mark(X2)) -> and(X1,X2) [19] and(active(X1),X2) -> and(X1,X2) [20] and(X1,active(X2)) -> and(X1,X2) [21] length(mark(X)) -> length(X) [22] length(active(X)) -> length(X) [23] s(mark(X)) -> s(X) [24] s(active(X)) -> s(X) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 5 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(0) >= active(0) ; mark(zeros) >= active(zeros) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(tt) >= active(tt) ; mark(length(X)) >= active(length(mark(X))) ; mark(nil) >= active(nil) ; mark(s(X)) >= active(s(mark(X))) ; cons(mark(X1),X2) >= cons(X1,X2) ; cons(active(X1),X2) >= cons(X1,X2) ; cons(X1,mark(X2)) >= cons(X1,X2) ; cons(X1,active(X2)) >= cons(X1,X2) ; active(zeros) >= mark(cons(0,zeros)) ; active(and(tt,X)) >= mark(X) ; active(length(cons(N,L))) >= mark(s(length(L))) ; active(length(nil)) >= mark(0) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; length(mark(X)) >= length(X) ; length(active(X)) >= length(X) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) ; Marked_mark(zeros) >= Marked_active(zeros) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(length(X)) >= Marked_mark(X) ; Marked_mark(length(X)) >= Marked_active(length(mark(X))) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_active(s(mark(X))) ; Marked_active(zeros) >= Marked_mark(cons(0,zeros)) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(length(cons(N,L))) >= Marked_mark(s(length(L))) ; } + Disjunctions:{ { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(cons(X1,X2)) > Marked_active(cons(mark(X1),X2)) ; } { Marked_mark(zeros) > Marked_active(zeros) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } { Marked_mark(length(X)) > Marked_active(length(mark(X))) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_active(s(mark(X))) ; } { Marked_active(zeros) > Marked_mark(cons(0,zeros)) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(length(cons(N,L))) > Marked_mark(s(length(L))) ; } } === 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: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(zeros) >= active(zeros) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(tt) >= active(tt) constraint: mark(length(X)) >= active(length(mark(X))) constraint: mark(nil) >= active(nil) constraint: mark(s(X)) >= active(s(mark(X))) constraint: cons(mark(X1),X2) >= cons(X1,X2) constraint: cons(active(X1),X2) >= cons(X1,X2) constraint: cons(X1,mark(X2)) >= cons(X1,X2) constraint: cons(X1,active(X2)) >= cons(X1,X2) constraint: active(zeros) >= mark(cons(0,zeros)) constraint: active(and(tt,X)) >= mark(X) constraint: active(length(cons(N,L))) >= mark(s(length(L))) constraint: active(length(nil)) >= mark(0) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: length(mark(X)) >= length(X) constraint: length(active(X)) >= length(X) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) constraint: Marked_mark(zeros) >= Marked_active(zeros) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(length(X)) >= Marked_mark(X) constraint: Marked_mark(length(X)) >= Marked_active(length(mark(X))) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(s(X)) >= Marked_active(s(mark(X))) constraint: Marked_active(zeros) >= Marked_mark(cons(0,zeros)) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(length(cons(N,L))) >= Marked_mark(s(length(L))) APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_and -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_length -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(0) >= active(0) ; mark(zeros) >= active(zeros) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(tt) >= active(tt) ; mark(length(X)) >= active(length(mark(X))) ; mark(nil) >= active(nil) ; mark(s(X)) >= active(s(mark(X))) ; cons(mark(X1),X2) >= cons(X1,X2) ; cons(active(X1),X2) >= cons(X1,X2) ; cons(X1,mark(X2)) >= cons(X1,X2) ; cons(X1,active(X2)) >= cons(X1,X2) ; active(zeros) >= mark(cons(0,zeros)) ; active(and(tt,X)) >= mark(X) ; active(length(cons(N,L))) >= mark(s(length(L))) ; active(length(nil)) >= mark(0) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; length(mark(X)) >= length(X) ; length(active(X)) >= length(X) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(zeros) >= Marked_active(zeros) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(length(X)) >= Marked_mark(X) ; Marked_mark(length(X)) >= Marked_active(length(mark(X))) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_active(zeros) >= Marked_mark(cons(0,zeros)) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(length(cons(N,L))) >= Marked_mark(s(length(L))) ; } + Disjunctions:{ { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(zeros) > Marked_active(zeros) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } { Marked_mark(length(X)) > Marked_active(length(mark(X))) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_active(zeros) > Marked_mark(cons(0,zeros)) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(length(cons(N,L))) > Marked_mark(s(length(L))) ; } } === 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: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(zeros) >= active(zeros) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(tt) >= active(tt) constraint: mark(length(X)) >= active(length(mark(X))) constraint: mark(nil) >= active(nil) constraint: mark(s(X)) >= active(s(mark(X))) constraint: cons(mark(X1),X2) >= cons(X1,X2) constraint: cons(active(X1),X2) >= cons(X1,X2) constraint: cons(X1,mark(X2)) >= cons(X1,X2) constraint: cons(X1,active(X2)) >= cons(X1,X2) constraint: active(zeros) >= mark(cons(0,zeros)) constraint: active(and(tt,X)) >= mark(X) constraint: active(length(cons(N,L))) >= mark(s(length(L))) constraint: active(length(nil)) >= mark(0) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: length(mark(X)) >= length(X) constraint: length(active(X)) >= length(X) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(zeros) >= Marked_active(zeros) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(length(X)) >= Marked_mark(X) constraint: Marked_mark(length(X)) >= Marked_active(length(mark(X))) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_active(zeros) >= Marked_mark(cons(0,zeros)) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(length(cons(N,L))) >= Marked_mark(s(length(L))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> -->