- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__zeros -> cons(0,zeros) [2] a__U11(tt,L) -> s(a__length(mark(L))) [3] a__and(tt,X) -> mark(X) [4] a__isNat(0) -> tt [5] a__isNat(length(V1)) -> a__isNatList(V1) [6] a__isNat(s(V1)) -> a__isNat(V1) [7] a__isNatIList(V) -> a__isNatList(V) [8] a__isNatIList(zeros) -> tt [9] a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) [10] a__isNatList(nil) -> tt [11] a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) [12] a__length(nil) -> 0 [13] a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) [14] mark(zeros) -> a__zeros [15] mark(U11(X1,X2)) -> a__U11(mark(X1),X2) [16] mark(length(X)) -> a__length(mark(X)) [17] mark(and(X1,X2)) -> a__and(mark(X1),X2) [18] mark(isNat(X)) -> a__isNat(X) [19] mark(isNatList(X)) -> a__isNatList(X) [20] mark(isNatIList(X)) -> a__isNatIList(X) [21] mark(cons(X1,X2)) -> cons(mark(X1),X2) [22] mark(0) -> 0 [23] mark(tt) -> tt [24] mark(s(X)) -> s(mark(X)) [25] mark(nil) -> nil [26] a__zeros -> zeros [27] a__U11(X1,X2) -> U11(X1,X2) [28] a__length(X) -> length(X) [29] a__and(X1,X2) -> and(X1,X2) [30] a__isNat(X) -> isNat(X) [31] a__isNatList(X) -> isNatList(X) [32] a__isNatIList(X) -> isNatIList(X) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(s(X)) >= s(mark(X)) ; mark(tt) >= tt ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIList(X)) >= a__isNatIList(X) ; mark(nil) >= nil ; mark(isNatList(X)) >= a__isNatList(X) ; mark(isNat(X)) >= a__isNat(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,L) >= s(a__length(mark(L))) ; a__U11(X1,X2) >= U11(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(length(V1)) >= a__isNatList(V1) ; a__isNat(X) >= isNat(X) ; a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) ; a__isNatList(nil) >= tt ; a__isNatList(X) >= isNatList(X) ; a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) ; a__isNatIList(zeros) >= tt ; a__isNatIList(X) >= isNatIList(X) ; a__isNatIList(V) >= a__isNatList(V) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__isNat(V1) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatIList(V2)) ; Marked_a__isNatIList(V) >= Marked_a__isNatList(V) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNat(V1) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1),isNatList(V2)) ; Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ; Marked_a__isNat(length(V1)) >= Marked_a__isNatList(V1) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_a__length(cons(N,L)) >= Marked_a__isNatList(L) ; Marked_a__length(cons(N,L)) >= Marked_a__and(a__isNatList(L),isNat(N)) ; Marked_a__length(cons(N,L)) >= Marked_a__U11(a__and(a__isNatList(L),isNat(N)), L) ; Marked_a__U11(tt,L) >= Marked_a__length(mark(L)) ; Marked_a__U11(tt,L) >= Marked_mark(L) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(length(X)) >= Marked_a__length(mark(X)) ; Marked_mark(length(X)) >= Marked_mark(X) ; Marked_mark(isNatIList(X)) >= Marked_a__isNatIList(X) ; Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__isNat(V1) ; } { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__and(a__isNat(V1), isNatIList(V2)) ; } { Marked_a__isNatIList(V) > Marked_a__isNatList(V) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__isNat(V1) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__and(a__isNat(V1),isNatList(V2)) ; } { Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(length(V1)) > Marked_a__isNatList(V1) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_a__length(cons(N,L)) > Marked_a__isNatList(L) ; } { Marked_a__length(cons(N,L)) > Marked_a__and(a__isNatList(L),isNat(N)) ; } { Marked_a__length(cons(N,L)) > Marked_a__U11(a__and(a__isNatList(L),isNat(N)), L) ; } { Marked_a__U11(tt,L) > Marked_a__length(mark(L)) ; } { Marked_a__U11(tt,L) > Marked_mark(L) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(length(X)) > Marked_a__length(mark(X)) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } { Marked_mark(isNatIList(X)) > Marked_a__isNatIList(X) ; } { Marked_mark(isNatList(X)) > Marked_a__isNatList(X) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === 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: a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(s(X)) >= s(mark(X)) constraint: mark(tt) >= tt constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(nil) >= nil constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,L) >= s(a__length(mark(L))) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(length(V1)) >= a__isNatList(V1) constraint: a__isNat(X) >= isNat(X) constraint: a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(X) >= isNatList(X) constraint: a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__isNatIList(V) >= a__isNatList(V) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__isNat(V1) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatIList(V2)) constraint: Marked_a__isNatIList(V) >= Marked_a__isNatList(V) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNat(V1) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatList(V2)) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(length(V1)) >= Marked_a__isNatList(V1) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_a__length(cons(N,L)) >= Marked_a__isNatList(L) constraint: Marked_a__length(cons(N,L)) >= Marked_a__and(a__isNatList(L), isNat(N)) constraint: Marked_a__length(cons(N,L)) >= Marked_a__U11(a__and(a__isNatList(L), isNat(N)),L) constraint: Marked_a__U11(tt,L) >= Marked_a__length(mark(L)) constraint: Marked_a__U11(tt,L) >= Marked_mark(L) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(length(X)) >= Marked_a__length(mark(X)) constraint: Marked_mark(length(X)) >= Marked_mark(X) constraint: Marked_mark(isNatIList(X)) >= Marked_a__isNatIList(X) constraint: Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(s(X)) >= s(mark(X)) ; mark(tt) >= tt ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIList(X)) >= a__isNatIList(X) ; mark(nil) >= nil ; mark(isNatList(X)) >= a__isNatList(X) ; mark(isNat(X)) >= a__isNat(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,L) >= s(a__length(mark(L))) ; a__U11(X1,X2) >= U11(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(length(V1)) >= a__isNatList(V1) ; a__isNat(X) >= isNat(X) ; a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) ; a__isNatList(nil) >= tt ; a__isNatList(X) >= isNatList(X) ; a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) ; a__isNatIList(zeros) >= tt ; a__isNatIList(X) >= isNatIList(X) ; a__isNatIList(V) >= a__isNatList(V) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatIList(V2)) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNat(V1) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1),isNatList(V2)) ; Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ; Marked_a__isNat(length(V1)) >= Marked_a__isNatList(V1) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_a__length(cons(N,L)) >= Marked_a__isNatList(L) ; Marked_a__length(cons(N,L)) >= Marked_a__and(a__isNatList(L),isNat(N)) ; Marked_a__length(cons(N,L)) >= Marked_a__U11(a__and(a__isNatList(L),isNat(N)), L) ; Marked_a__U11(tt,L) >= Marked_a__length(mark(L)) ; Marked_a__U11(tt,L) >= Marked_mark(L) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(length(X)) >= Marked_a__length(mark(X)) ; Marked_mark(length(X)) >= Marked_mark(X) ; Marked_mark(isNatIList(X)) >= Marked_a__isNatIList(X) ; Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__and(a__isNat(V1), isNatIList(V2)) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__isNat(V1) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__and(a__isNat(V1),isNatList(V2)) ; } { Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(length(V1)) > Marked_a__isNatList(V1) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_a__length(cons(N,L)) > Marked_a__isNatList(L) ; } { Marked_a__length(cons(N,L)) > Marked_a__and(a__isNatList(L),isNat(N)) ; } { Marked_a__length(cons(N,L)) > Marked_a__U11(a__and(a__isNatList(L),isNat(N)), L) ; } { Marked_a__U11(tt,L) > Marked_a__length(mark(L)) ; } { Marked_a__U11(tt,L) > Marked_mark(L) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(length(X)) > Marked_a__length(mark(X)) ; } { Marked_mark(length(X)) > Marked_mark(X) ; } { Marked_mark(isNatIList(X)) > Marked_a__isNatIList(X) ; } { Marked_mark(isNatList(X)) > Marked_a__isNatList(X) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === 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: a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(s(X)) >= s(mark(X)) constraint: mark(tt) >= tt constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(nil) >= nil constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,L) >= s(a__length(mark(L))) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(length(V1)) >= a__isNatList(V1) constraint: a__isNat(X) >= isNat(X) constraint: a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(X) >= isNatList(X) constraint: a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__isNatIList(V) >= a__isNatList(V) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatIList(V2)) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNat(V1) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatList(V2)) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(length(V1)) >= Marked_a__isNatList(V1) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_a__length(cons(N,L)) >= Marked_a__isNatList(L) constraint: Marked_a__length(cons(N,L)) >= Marked_a__and(a__isNatList(L), isNat(N)) constraint: Marked_a__length(cons(N,L)) >= Marked_a__U11(a__and(a__isNatList(L), isNat(N)),L) constraint: Marked_a__U11(tt,L) >= Marked_a__length(mark(L)) constraint: Marked_a__U11(tt,L) >= Marked_mark(L) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(length(X)) >= Marked_a__length(mark(X)) constraint: Marked_mark(length(X)) >= Marked_mark(X) constraint: Marked_mark(isNatIList(X)) >= Marked_a__isNatIList(X) constraint: Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(s(X)) >= s(mark(X)) ; mark(tt) >= tt ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIList(X)) >= a__isNatIList(X) ; mark(nil) >= nil ; mark(isNatList(X)) >= a__isNatList(X) ; mark(isNat(X)) >= a__isNat(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,L) >= s(a__length(mark(L))) ; a__U11(X1,X2) >= U11(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(length(V1)) >= a__isNatList(V1) ; a__isNat(X) >= isNat(X) ; a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) ; a__isNatList(nil) >= tt ; a__isNatList(X) >= isNatList(X) ; a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) ; a__isNatIList(zeros) >= tt ; a__isNatIList(X) >= isNatIList(X) ; a__isNatIList(V) >= a__isNatList(V) ; Marked_a__length(cons(N,L)) >= Marked_a__U11(a__and(a__isNatList(L),isNat(N)), L) ; Marked_a__U11(tt,L) >= Marked_a__length(mark(L)) ; } + Disjunctions:{ { Marked_a__length(cons(N,L)) > Marked_a__U11(a__and(a__isNatList(L),isNat(N)), L) ; } { Marked_a__U11(tt,L) > Marked_a__length(mark(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: a__zeros >= cons(0,zeros) constraint: a__zeros >= zeros constraint: a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(s(X)) >= s(mark(X)) constraint: mark(tt) >= tt constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(nil) >= nil constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,L) >= s(a__length(mark(L))) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(length(V1)) >= a__isNatList(V1) constraint: a__isNat(X) >= isNat(X) constraint: a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(X) >= isNatList(X) constraint: a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__isNatIList(V) >= a__isNatList(V) constraint: Marked_a__length(cons(N,L)) >= Marked_a__U11(a__and(a__isNatList(L), isNat(N)),L) constraint: Marked_a__U11(tt,L) >= Marked_a__length(mark(L)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(s(X)) >= s(mark(X)) ; mark(tt) >= tt ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIList(X)) >= a__isNatIList(X) ; mark(nil) >= nil ; mark(isNatList(X)) >= a__isNatList(X) ; mark(isNat(X)) >= a__isNat(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,L) >= s(a__length(mark(L))) ; a__U11(X1,X2) >= U11(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(length(V1)) >= a__isNatList(V1) ; a__isNat(X) >= isNat(X) ; a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) ; a__isNatList(nil) >= tt ; a__isNatList(X) >= isNatList(X) ; a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) ; a__isNatIList(zeros) >= tt ; a__isNatIList(X) >= isNatIList(X) ; a__isNatIList(V) >= a__isNatList(V) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatIList(V2)) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNat(V1) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1),isNatList(V2)) ; Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ; Marked_a__isNat(length(V1)) >= Marked_a__isNatList(V1) ; 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(isNatIList(X)) >= Marked_a__isNatIList(X) ; Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__and(a__isNat(V1), isNatIList(V2)) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__isNat(V1) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__and(a__isNat(V1),isNatList(V2)) ; } { Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(length(V1)) > Marked_a__isNatList(V1) ; } { 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(isNatIList(X)) > Marked_a__isNatIList(X) ; } { Marked_mark(isNatList(X)) > Marked_a__isNatList(X) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === 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: a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(s(X)) >= s(mark(X)) constraint: mark(tt) >= tt constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(nil) >= nil constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,L) >= s(a__length(mark(L))) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(length(V1)) >= a__isNatList(V1) constraint: a__isNat(X) >= isNat(X) constraint: a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(X) >= isNatList(X) constraint: a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__isNatIList(V) >= a__isNatList(V) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatIList(V2)) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__isNat(V1) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatList(V2)) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(length(V1)) >= Marked_a__isNatList(V1) 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(isNatIList(X)) >= Marked_a__isNatIList(X) constraint: Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(s(X)) >= s(mark(X)) ; mark(tt) >= tt ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIList(X)) >= a__isNatIList(X) ; mark(nil) >= nil ; mark(isNatList(X)) >= a__isNatList(X) ; mark(isNat(X)) >= a__isNat(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,L) >= s(a__length(mark(L))) ; a__U11(X1,X2) >= U11(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(length(V1)) >= a__isNatList(V1) ; a__isNat(X) >= isNat(X) ; a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) ; a__isNatList(nil) >= tt ; a__isNatList(X) >= isNatList(X) ; a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) ; a__isNatIList(zeros) >= tt ; a__isNatIList(X) >= isNatIList(X) ; a__isNatIList(V) >= a__isNatList(V) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatIList(V2)) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1),isNatList(V2)) ; 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(isNatIList(X)) >= Marked_a__isNatIList(X) ; Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__and(a__isNat(V1), isNatIList(V2)) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__and(a__isNat(V1),isNatList(V2)) ; } { 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(isNatIList(X)) > Marked_a__isNatIList(X) ; } { Marked_mark(isNatList(X)) > Marked_a__isNatList(X) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === 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: a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(s(X)) >= s(mark(X)) constraint: mark(tt) >= tt constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(nil) >= nil constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,L) >= s(a__length(mark(L))) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(length(V1)) >= a__isNatList(V1) constraint: a__isNat(X) >= isNat(X) constraint: a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(X) >= isNatList(X) constraint: a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__isNatIList(V) >= a__isNatList(V) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatIList(V2)) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatList(V2)) 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(isNatIList(X)) >= Marked_a__isNatIList(X) constraint: Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(s(X)) >= s(mark(X)) ; mark(tt) >= tt ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIList(X)) >= a__isNatIList(X) ; mark(nil) >= nil ; mark(isNatList(X)) >= a__isNatList(X) ; mark(isNat(X)) >= a__isNat(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,L) >= s(a__length(mark(L))) ; a__U11(X1,X2) >= U11(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(length(V1)) >= a__isNatList(V1) ; a__isNat(X) >= isNat(X) ; a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) ; a__isNatList(nil) >= tt ; a__isNatList(X) >= isNatList(X) ; a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) ; a__isNatIList(zeros) >= tt ; a__isNatIList(X) >= isNatIList(X) ; a__isNatIList(V) >= a__isNatList(V) ; Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ; } + Disjunctions:{ { Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ; } } === 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: a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(s(X)) >= s(mark(X)) constraint: mark(tt) >= tt constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(nil) >= nil constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,L) >= s(a__length(mark(L))) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(length(V1)) >= a__isNatList(V1) constraint: a__isNat(X) >= isNat(X) constraint: a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(X) >= isNatList(X) constraint: a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__isNatIList(V) >= a__isNatList(V) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(s(X)) >= s(mark(X)) ; mark(tt) >= tt ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIList(X)) >= a__isNatIList(X) ; mark(nil) >= nil ; mark(isNatList(X)) >= a__isNatList(X) ; mark(isNat(X)) >= a__isNat(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,L) >= s(a__length(mark(L))) ; a__U11(X1,X2) >= U11(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(length(V1)) >= a__isNatList(V1) ; a__isNat(X) >= isNat(X) ; a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) ; a__isNatList(nil) >= tt ; a__isNatList(X) >= isNatList(X) ; a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) ; a__isNatIList(zeros) >= tt ; a__isNatIList(X) >= isNatIList(X) ; a__isNatIList(V) >= a__isNatList(V) ; Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatIList(V2)) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1),isNatList(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(isNatIList(X)) >= Marked_a__isNatIList(X) ; Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNatIList(cons(V1,V2)) > Marked_a__and(a__isNat(V1), isNatIList(V2)) ; } { Marked_a__isNatList(cons(V1,V2)) > Marked_a__and(a__isNat(V1),isNatList(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(isNatIList(X)) > Marked_a__isNatIList(X) ; } { Marked_mark(isNatList(X)) > Marked_a__isNatList(X) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === 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: a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(s(X)) >= s(mark(X)) constraint: mark(tt) >= tt constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(nil) >= nil constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,L) >= s(a__length(mark(L))) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(length(V1)) >= a__isNatList(V1) constraint: a__isNat(X) >= isNat(X) constraint: a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(X) >= isNatList(X) constraint: a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__isNatIList(V) >= a__isNatList(V) constraint: Marked_a__isNatIList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatIList(V2)) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatList(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(isNatIList(X)) >= Marked_a__isNatIList(X) constraint: Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(s(X)) >= s(mark(X)) ; mark(tt) >= tt ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIList(X)) >= a__isNatIList(X) ; mark(nil) >= nil ; mark(isNatList(X)) >= a__isNatList(X) ; mark(isNat(X)) >= a__isNat(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,L) >= s(a__length(mark(L))) ; a__U11(X1,X2) >= U11(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(length(V1)) >= a__isNatList(V1) ; a__isNat(X) >= isNat(X) ; a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) ; a__isNatList(nil) >= tt ; a__isNatList(X) >= isNatList(X) ; a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) ; a__isNatIList(zeros) >= tt ; a__isNatIList(X) >= isNatIList(X) ; a__isNatIList(V) >= a__isNatList(V) ; Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1),isNatList(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNatList(cons(V1,V2)) > Marked_a__and(a__isNat(V1),isNatList(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(isNatList(X)) > Marked_a__isNatList(X) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === 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: a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(s(X)) >= s(mark(X)) constraint: mark(tt) >= tt constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(nil) >= nil constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,L) >= s(a__length(mark(L))) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(length(V1)) >= a__isNatList(V1) constraint: a__isNat(X) >= isNat(X) constraint: a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(X) >= isNatList(X) constraint: a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__isNatIList(V) >= a__isNatList(V) constraint: Marked_a__isNatList(cons(V1,V2)) >= Marked_a__and(a__isNat(V1), isNatList(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(isNatList(X)) >= Marked_a__isNatList(X) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) ; a__length(nil) >= 0 ; a__length(X) >= length(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(s(X)) >= s(mark(X)) ; mark(tt) >= tt ; mark(length(X)) >= a__length(mark(X)) ; mark(isNatIList(X)) >= a__isNatIList(X) ; mark(nil) >= nil ; mark(isNatList(X)) >= a__isNatList(X) ; mark(isNat(X)) >= a__isNat(X) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,L) >= s(a__length(mark(L))) ; a__U11(X1,X2) >= U11(X1,X2) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(0) >= tt ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(length(V1)) >= a__isNatList(V1) ; a__isNat(X) >= isNat(X) ; a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) ; a__isNatList(nil) >= tt ; a__isNatList(X) >= isNatList(X) ; a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) ; a__isNatIList(zeros) >= tt ; a__isNatIList(X) >= isNatIList(X) ; a__isNatIList(V) >= a__isNatList(V) ; Marked_mark(s(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_mark(s(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: a__length(cons(N,L)) >= a__U11(a__and(a__isNatList(L),isNat(N)),L) constraint: a__length(nil) >= 0 constraint: a__length(X) >= length(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(s(X)) >= s(mark(X)) constraint: mark(tt) >= tt constraint: mark(length(X)) >= a__length(mark(X)) constraint: mark(isNatIList(X)) >= a__isNatIList(X) constraint: mark(nil) >= nil constraint: mark(isNatList(X)) >= a__isNatList(X) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,L) >= s(a__length(mark(L))) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(0) >= tt constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(length(V1)) >= a__isNatList(V1) constraint: a__isNat(X) >= isNat(X) constraint: a__isNatList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatList(V2)) constraint: a__isNatList(nil) >= tt constraint: a__isNatList(X) >= isNatList(X) constraint: a__isNatIList(cons(V1,V2)) >= a__and(a__isNat(V1),isNatIList(V2)) constraint: a__isNatIList(zeros) >= tt constraint: a__isNatIList(X) >= isNatIList(X) constraint: a__isNatIList(V) >= a__isNatList(V) constraint: Marked_mark(s(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a__zeros -> cons(0,zeros) [2] a__U11(tt,L) -> s(a__length(mark(L))) [3] a__and(tt,X) -> mark(X) [4] a__isNat(0) -> tt [5] a__isNat(length(V1)) -> a__isNatList(V1) [6] a__isNat(s(V1)) -> a__isNat(V1) [7] a__isNatIList(V) -> a__isNatList(V) [8] a__isNatIList(zeros) -> tt [9] a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) [10] a__isNatList(nil) -> tt [11] a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) [12] a__length(nil) -> 0 [13] a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) [14] mark(zeros) -> a__zeros [15] mark(U11(X1,X2)) -> a__U11(mark(X1),X2) [16] mark(length(X)) -> a__length(mark(X)) [17] mark(and(X1,X2)) -> a__and(mark(X1),X2) [18] mark(isNat(X)) -> a__isNat(X) [19] mark(isNatList(X)) -> a__isNatList(X) [20] mark(isNatIList(X)) -> a__isNatIList(X) [21] mark(cons(X1,X2)) -> cons(mark(X1),X2) [22] mark(0) -> 0 [23] mark(tt) -> tt [24] mark(s(X)) -> s(mark(X)) [25] mark(nil) -> nil [26] a__zeros -> zeros [27] a__U11(X1,X2) -> U11(X1,X2) [28] a__length(X) -> length(X) [29] a__and(X1,X2) -> and(X1,X2) [30] a__isNat(X) -> isNat(X) [31] a__isNatList(X) -> isNatList(X) [32] a__isNatIList(X) -> isNatIList(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ cons ] (X0,X1) = 2*X1 + 1*X0; [ isNatList ] (X0) = 0; [ tt ] () = 0; [ Marked_a__length ] (X0) = 1*X0; [ s ] (X0) = 1*X0; [ Marked_a__isNatIList ] (X0) = 2; [ length ] (X0) = 1*X0; [ zeros ] () = 0; [ U11 ] (X0,X1) = 1*X1 + 2*X0; [ a__isNat ] (X0) = 0; [ mark ] (X0) = 2*X0; [ Marked_a__isNat ] (X0) = 0; [ isNatIList ] (X0) = 1; [ 0 ] () = 0; [ isNat ] (X0) = 0; [ a__and ] (X0,X1) = 2*X1 + 2*X0; [ Marked_a__U11 ] (X0,X1) = 2*X1; [ a__length ] (X0) = 1*X0; [ Marked_a__isNatList ] (X0) = 0; [ a__isNatIList ] (X0) = 2; [ a__zeros ] () = 0; [ and ] (X0,X1) = 2*X1 + 2*X0; [ a__isNatList ] (X0) = 0; [ Marked_mark ] (X0) = 2*X0; [ a__U11 ] (X0,X1) = 2*X1 + 2*X0; [ Marked_a__and ] (X0,X1) = 2*X1; [ nil ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ cons ] (X0,X1) = 2*X1 + 2*X0; [ isNatList ] (X0) = 0; [ tt ] () = 0; [ Marked_a__length ] (X0) = 2*X0; [ s ] (X0) = 1*X0; [ Marked_a__isNatIList ] (X0) = 0; [ length ] (X0) = 1*X0 + 2; [ zeros ] () = 0; [ U11 ] (X0,X1) = 2*X1 + 2*X0 + 2; [ a__isNat ] (X0) = 0; [ mark ] (X0) = 1*X0; [ Marked_a__isNat ] (X0) = 0; [ isNatIList ] (X0) = 0; [ 0 ] () = 0; [ isNat ] (X0) = 0; [ a__and ] (X0,X1) = 2*X1 + 2*X0; [ Marked_a__U11 ] (X0,X1) = 2*X1; [ a__length ] (X0) = 1*X0 + 2; [ Marked_a__isNatList ] (X0) = 0; [ a__isNatIList ] (X0) = 0; [ a__zeros ] () = 0; [ and ] (X0,X1) = 2*X1 + 2*X0; [ a__isNatList ] (X0) = 0; [ Marked_mark ] (X0) = 2*X0; [ a__U11 ] (X0,X1) = 2*X1 + 2*X0 + 2; [ Marked_a__and ] (X0,X1) = 2*X1; [ nil ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ cons ] (X0,X1) = 2*X1 + 1*X0 + 1; [ isNatList ] (X0) = 1*X0; [ tt ] () = 2; [ Marked_a__length ] (X0) = 2*X0; [ s ] (X0) = 1*X0 + 1; [ length ] (X0) = 1*X0; [ zeros ] () = 0; [ U11 ] (X0,X1) = 1*X1 + 1*X0 + 1; [ a__isNat ] (X0) = 1*X0 + 1; [ mark ] (X0) = 1*X0 + 2; [ isNatIList ] (X0) = 2*X0; [ 0 ] () = 1; [ isNat ] (X0) = 1*X0; [ a__and ] (X0,X1) = 1*X1 + 1*X0; [ Marked_a__U11 ] (X0,X1) = 2*X1 + 2*X0; [ a__length ] (X0) = 1*X0; [ a__isNatIList ] (X0) = 2*X0 + 2; [ a__zeros ] () = 2; [ and ] (X0,X1) = 1*X1 + 1*X0; [ a__isNatList ] (X0) = 1*X0; [ a__U11 ] (X0,X1) = 1*X1 + 1*X0 + 1; [ nil ] () = 2; removing [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ cons ] (X0,X1) = 2*X1 + 1*X0; [ isNatList ] (X0) = 1*X0; [ tt ] () = 0; [ s ] (X0) = 1*X0; [ Marked_a__isNatIList ] (X0) = 2*X0; [ length ] (X0) = 1*X0 + 2; [ zeros ] () = 0; [ U11 ] (X0,X1) = 2*X1 + 1; [ a__isNat ] (X0) = 1*X0; [ mark ] (X0) = 2*X0; [ Marked_a__isNat ] (X0) = 1*X0; [ isNatIList ] (X0) = 2*X0; [ 0 ] () = 0; [ isNat ] (X0) = 1*X0; [ a__and ] (X0,X1) = 2*X1 + 1*X0; [ a__length ] (X0) = 1*X0 + 2; [ Marked_a__isNatList ] (X0) = 1*X0; [ a__isNatIList ] (X0) = 2*X0; [ a__zeros ] () = 0; [ and ] (X0,X1) = 1*X1 + 1*X0; [ a__isNatList ] (X0) = 1*X0; [ Marked_mark ] (X0) = 1*X0; [ a__U11 ] (X0,X1) = 2*X1 + 2; [ Marked_a__and ] (X0,X1) = 1*X1; [ nil ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ cons ] (X0,X1) = 1*X0 + 2; [ isNatList ] (X0) = 0; [ tt ] () = 0; [ s ] (X0) = 1*X0; [ Marked_a__isNatIList ] (X0) = 0; [ length ] (X0) = 0; [ zeros ] () = 2; [ U11 ] (X0,X1) = 0; [ a__isNat ] (X0) = 0; [ mark ] (X0) = 1*X0; [ isNatIList ] (X0) = 0; [ 0 ] () = 0; [ isNat ] (X0) = 0; [ a__and ] (X0,X1) = 2*X1 + 2*X0; [ a__length ] (X0) = 0; [ Marked_a__isNatList ] (X0) = 0; [ a__isNatIList ] (X0) = 0; [ a__zeros ] () = 2; [ and ] (X0,X1) = 2*X1 + 2*X0; [ a__isNatList ] (X0) = 0; [ Marked_mark ] (X0) = 1*X0; [ a__U11 ] (X0,X1) = 0; [ Marked_a__and ] (X0,X1) = 1*X1; [ nil ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ cons ] (X0,X1) = 1*X1 + 1; [ isNatList ] (X0) = 0; [ tt ] () = 0; [ s ] (X0) = 1*X0; [ Marked_a__isNatIList ] (X0) = 1*X0; [ length ] (X0) = 0; [ zeros ] () = 1; [ U11 ] (X0,X1) = 0; [ a__isNat ] (X0) = 0; [ mark ] (X0) = 2*X0; [ isNatIList ] (X0) = 1*X0; [ 0 ] () = 0; [ isNat ] (X0) = 0; [ a__and ] (X0,X1) = 2*X1 + 2*X0; [ a__length ] (X0) = 0; [ Marked_a__isNatList ] (X0) = 0; [ a__isNatIList ] (X0) = 2*X0; [ a__zeros ] () = 2; [ and ] (X0,X1) = 1*X1 + 2*X0; [ a__isNatList ] (X0) = 0; [ Marked_mark ] (X0) = 1*X0; [ a__U11 ] (X0,X1) = 0; [ Marked_a__and ] (X0,X1) = 1*X1; [ nil ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ cons ] (X0,X1) = 2*X1 + 1*X0 + 2; [ isNatList ] (X0) = 2*X0 + 1; [ tt ] () = 0; [ s ] (X0) = 1*X0; [ length ] (X0) = 1*X0 + 1; [ zeros ] () = 0; [ U11 ] (X0,X1) = 1*X1 + 1; [ a__isNat ] (X0) = 2*X0; [ mark ] (X0) = 1*X0 + 2; [ isNatIList ] (X0) = 2*X0; [ 0 ] () = 0; [ isNat ] (X0) = 2*X0; [ a__and ] (X0,X1) = 2*X1 + 1*X0 + 3; [ a__length ] (X0) = 1*X0 + 1; [ Marked_a__isNatList ] (X0) = 2*X0; [ a__isNatIList ] (X0) = 2*X0 + 1; [ a__zeros ] () = 2; [ and ] (X0,X1) = 2*X1 + 1*X0 + 3; [ a__isNatList ] (X0) = 2*X0 + 1; [ Marked_mark ] (X0) = 1*X0 + 1; [ a__U11 ] (X0,X1) = 1*X1 + 3; [ Marked_a__and ] (X0,X1) = 1*X1 + 2; [ nil ] () = 0; removing < Marked_mark(and(X1,X2)),Marked_mark(X1)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ cons ] (X0,X1) = 2 + 2*X0 + 3*X1 + 0; [ isNatList ] (X0) = 1*X0 + 0; [ tt ] () = 2 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ length ] (X0) = 1*X0 + 0; [ zeros ] () = 0; [ U11 ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; [ a__isNat ] (X0) = 2 + 2*X0 + 0; [ mark ] (X0) = 2 + 2*X0 + 0; [ isNatIList ] (X0) = 1*X0 + 0; [ 0 ] () = 0; [ isNat ] (X0) = 1*X0 + 0; [ a__and ] (X0,X1) = 1*X0 + 2*X1 + 0; [ a__length ] (X0) = 1*X0 + 0; [ a__isNatIList ] (X0) = 2 + 2*X0 + 0; [ a__zeros ] () = 2 + 0; [ and ] (X0,X1) = 1*X0 + 2*X1 + 0; [ a__isNatList ] (X0) = 1*X0 + 0; [ Marked_mark ] (X0) = 3*X0 + 0; [ a__U11 ] (X0,X1) = 1 + 1*X0 + 2*X1 + 0; [ nil ] () = 2 + 0; ]} ]} ]} ]} ]} ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ cons ] (X0,X1) = 2 + 1*X0 + 2*X1 + 0; [ isNatList ] (X0) = 1*X0 + 0; [ tt ] () = 2 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ length ] (X0) = 1*X0 + 0; [ zeros ] () = 0; [ U11 ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; [ a__isNat ] (X0) = 2 + 1*X0 + 0; [ mark ] (X0) = 2 + 1*X0 + 0; [ Marked_a__isNat ] (X0) = 3*X0 + 0; [ isNatIList ] (X0) = 1*X0 + 0; [ 0 ] () = 0; [ isNat ] (X0) = 1*X0 + 0; [ a__and ] (X0,X1) = 1*X0 + 1*X1 + 0; [ a__length ] (X0) = 1*X0 + 0; [ a__isNatIList ] (X0) = 2 + 1*X0 + 0; [ a__zeros ] () = 2 + 0; [ and ] (X0,X1) = 1*X0 + 1*X1 + 0; [ a__isNatList ] (X0) = 1*X0 + 0; [ a__U11 ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; [ nil ] () = 2 + 0; ]} ]} ]} ]} ]} ]} ]} ]} ]} Cime worked for 1.202784 seconds (real time) Cime Exit Status: 0