- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__incr(nil) -> nil [2] a__incr(cons(X,L)) -> cons(s(mark(X)),incr(L)) [3] a__adx(nil) -> nil [4] a__adx(cons(X,L)) -> a__incr(cons(mark(X),adx(L))) [5] a__nats -> a__adx(a__zeros) [6] a__zeros -> cons(0,zeros) [7] a__head(cons(X,L)) -> mark(X) [8] a__tail(cons(X,L)) -> mark(L) [9] mark(incr(X)) -> a__incr(mark(X)) [10] mark(adx(X)) -> a__adx(mark(X)) [11] mark(nats) -> a__nats [12] mark(zeros) -> a__zeros [13] mark(head(X)) -> a__head(mark(X)) [14] mark(tail(X)) -> a__tail(mark(X)) [15] mark(nil) -> nil [16] mark(cons(X1,X2)) -> cons(mark(X1),X2) [17] mark(s(X)) -> s(mark(X)) [18] mark(0) -> 0 [19] a__incr(X) -> incr(X) [20] a__adx(X) -> adx(X) [21] a__nats -> nats [22] a__zeros -> zeros [23] a__head(X) -> head(X) [24] a__tail(X) -> tail(X) 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__incr(nil) >= nil ; a__incr(cons(X,L)) >= cons(s(mark(X)),incr(L)) ; a__incr(X) >= incr(X) ; mark(nil) >= nil ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(s(X)) >= s(mark(X)) ; mark(incr(X)) >= a__incr(mark(X)) ; mark(adx(X)) >= a__adx(mark(X)) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(nats) >= a__nats ; mark(head(X)) >= a__head(mark(X)) ; mark(tail(X)) >= a__tail(mark(X)) ; a__adx(nil) >= nil ; a__adx(cons(X,L)) >= a__incr(cons(mark(X),adx(L))) ; a__adx(X) >= adx(X) ; a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__nats >= a__adx(a__zeros) ; a__nats >= nats ; a__head(cons(X,L)) >= mark(X) ; a__head(X) >= head(X) ; a__tail(cons(X,L)) >= mark(L) ; a__tail(X) >= tail(X) ; Marked_a__tail(cons(X,L)) >= Marked_mark(L) ; Marked_a__head(cons(X,L)) >= Marked_mark(X) ; Marked_a__nats >= Marked_a__adx(a__zeros) ; Marked_a__adx(cons(X,L)) >= Marked_a__incr(cons(mark(X),adx(L))) ; Marked_a__adx(cons(X,L)) >= Marked_mark(X) ; Marked_a__incr(cons(X,L)) >= Marked_mark(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(incr(X)) >= Marked_a__incr(mark(X)) ; Marked_mark(incr(X)) >= Marked_mark(X) ; Marked_mark(adx(X)) >= Marked_a__adx(mark(X)) ; Marked_mark(adx(X)) >= Marked_mark(X) ; Marked_mark(nats) >= Marked_a__nats ; Marked_mark(head(X)) >= Marked_a__head(mark(X)) ; Marked_mark(head(X)) >= Marked_mark(X) ; Marked_mark(tail(X)) >= Marked_a__tail(mark(X)) ; Marked_mark(tail(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__tail(cons(X,L)) > Marked_mark(L) ; } { Marked_a__head(cons(X,L)) > Marked_mark(X) ; } { Marked_a__nats > Marked_a__adx(a__zeros) ; } { Marked_a__adx(cons(X,L)) > Marked_a__incr(cons(mark(X),adx(L))) ; } { Marked_a__adx(cons(X,L)) > Marked_mark(X) ; } { Marked_a__incr(cons(X,L)) > Marked_mark(X) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(incr(X)) > Marked_a__incr(mark(X)) ; } { Marked_mark(incr(X)) > Marked_mark(X) ; } { Marked_mark(adx(X)) > Marked_a__adx(mark(X)) ; } { Marked_mark(adx(X)) > Marked_mark(X) ; } { Marked_mark(nats) > Marked_a__nats ; } { Marked_mark(head(X)) > Marked_a__head(mark(X)) ; } { Marked_mark(head(X)) > Marked_mark(X) ; } { Marked_mark(tail(X)) > Marked_a__tail(mark(X)) ; } { Marked_mark(tail(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__incr(nil) >= nil constraint: a__incr(cons(X,L)) >= cons(s(mark(X)),incr(L)) constraint: a__incr(X) >= incr(X) constraint: mark(nil) >= nil constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(s(X)) >= s(mark(X)) constraint: mark(incr(X)) >= a__incr(mark(X)) constraint: mark(adx(X)) >= a__adx(mark(X)) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(nats) >= a__nats constraint: mark(head(X)) >= a__head(mark(X)) constraint: mark(tail(X)) >= a__tail(mark(X)) constraint: a__adx(nil) >= nil constraint: a__adx(cons(X,L)) >= a__incr(cons(mark(X),adx(L))) constraint: a__adx(X) >= adx(X) constraint: a__zeros >= cons(0,zeros) constraint: a__zeros >= zeros constraint: a__nats >= a__adx(a__zeros) constraint: a__nats >= nats constraint: a__head(cons(X,L)) >= mark(X) constraint: a__head(X) >= head(X) constraint: a__tail(cons(X,L)) >= mark(L) constraint: a__tail(X) >= tail(X) constraint: Marked_a__tail(cons(X,L)) >= Marked_mark(L) constraint: Marked_a__head(cons(X,L)) >= Marked_mark(X) constraint: Marked_a__nats >= Marked_a__adx(a__zeros) constraint: Marked_a__adx(cons(X,L)) >= Marked_a__incr(cons(mark(X),adx(L))) constraint: Marked_a__adx(cons(X,L)) >= Marked_mark(X) constraint: Marked_a__incr(cons(X,L)) >= Marked_mark(X) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(incr(X)) >= Marked_a__incr(mark(X)) constraint: Marked_mark(incr(X)) >= Marked_mark(X) constraint: Marked_mark(adx(X)) >= Marked_a__adx(mark(X)) constraint: Marked_mark(adx(X)) >= Marked_mark(X) constraint: Marked_mark(nats) >= Marked_a__nats constraint: Marked_mark(head(X)) >= Marked_a__head(mark(X)) constraint: Marked_mark(head(X)) >= Marked_mark(X) constraint: Marked_mark(tail(X)) >= Marked_a__tail(mark(X)) constraint: Marked_mark(tail(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__incr(nil) >= nil ; a__incr(cons(X,L)) >= cons(s(mark(X)),incr(L)) ; a__incr(X) >= incr(X) ; mark(nil) >= nil ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(s(X)) >= s(mark(X)) ; mark(incr(X)) >= a__incr(mark(X)) ; mark(adx(X)) >= a__adx(mark(X)) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(nats) >= a__nats ; mark(head(X)) >= a__head(mark(X)) ; mark(tail(X)) >= a__tail(mark(X)) ; a__adx(nil) >= nil ; a__adx(cons(X,L)) >= a__incr(cons(mark(X),adx(L))) ; a__adx(X) >= adx(X) ; a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__nats >= a__adx(a__zeros) ; a__nats >= nats ; a__head(cons(X,L)) >= mark(X) ; a__head(X) >= head(X) ; a__tail(cons(X,L)) >= mark(L) ; a__tail(X) >= tail(X) ; Marked_a__adx(cons(X,L)) >= Marked_a__incr(cons(mark(X),adx(L))) ; Marked_a__adx(cons(X,L)) >= Marked_mark(X) ; Marked_a__incr(cons(X,L)) >= Marked_mark(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(incr(X)) >= Marked_a__incr(mark(X)) ; Marked_mark(incr(X)) >= Marked_mark(X) ; Marked_mark(adx(X)) >= Marked_a__adx(mark(X)) ; Marked_mark(adx(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__adx(cons(X,L)) > Marked_a__incr(cons(mark(X),adx(L))) ; } { Marked_a__adx(cons(X,L)) > Marked_mark(X) ; } { Marked_a__incr(cons(X,L)) > Marked_mark(X) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(incr(X)) > Marked_a__incr(mark(X)) ; } { Marked_mark(incr(X)) > Marked_mark(X) ; } { Marked_mark(adx(X)) > Marked_a__adx(mark(X)) ; } { Marked_mark(adx(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__incr(nil) >= nil constraint: a__incr(cons(X,L)) >= cons(s(mark(X)),incr(L)) constraint: a__incr(X) >= incr(X) constraint: mark(nil) >= nil constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(s(X)) >= s(mark(X)) constraint: mark(incr(X)) >= a__incr(mark(X)) constraint: mark(adx(X)) >= a__adx(mark(X)) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(nats) >= a__nats constraint: mark(head(X)) >= a__head(mark(X)) constraint: mark(tail(X)) >= a__tail(mark(X)) constraint: a__adx(nil) >= nil constraint: a__adx(cons(X,L)) >= a__incr(cons(mark(X),adx(L))) constraint: a__adx(X) >= adx(X) constraint: a__zeros >= cons(0,zeros) constraint: a__zeros >= zeros constraint: a__nats >= a__adx(a__zeros) constraint: a__nats >= nats constraint: a__head(cons(X,L)) >= mark(X) constraint: a__head(X) >= head(X) constraint: a__tail(cons(X,L)) >= mark(L) constraint: a__tail(X) >= tail(X) constraint: Marked_a__adx(cons(X,L)) >= Marked_a__incr(cons(mark(X),adx(L))) constraint: Marked_a__adx(cons(X,L)) >= Marked_mark(X) constraint: Marked_a__incr(cons(X,L)) >= Marked_mark(X) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(incr(X)) >= Marked_a__incr(mark(X)) constraint: Marked_mark(incr(X)) >= Marked_mark(X) constraint: Marked_mark(adx(X)) >= Marked_a__adx(mark(X)) constraint: Marked_mark(adx(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__incr(nil) >= nil ; a__incr(cons(X,L)) >= cons(s(mark(X)),incr(L)) ; a__incr(X) >= incr(X) ; mark(nil) >= nil ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(s(X)) >= s(mark(X)) ; mark(incr(X)) >= a__incr(mark(X)) ; mark(adx(X)) >= a__adx(mark(X)) ; mark(0) >= 0 ; mark(zeros) >= a__zeros ; mark(nats) >= a__nats ; mark(head(X)) >= a__head(mark(X)) ; mark(tail(X)) >= a__tail(mark(X)) ; a__adx(nil) >= nil ; a__adx(cons(X,L)) >= a__incr(cons(mark(X),adx(L))) ; a__adx(X) >= adx(X) ; a__zeros >= cons(0,zeros) ; a__zeros >= zeros ; a__nats >= a__adx(a__zeros) ; a__nats >= nats ; a__head(cons(X,L)) >= mark(X) ; a__head(X) >= head(X) ; a__tail(cons(X,L)) >= mark(L) ; a__tail(X) >= tail(X) ; Marked_a__incr(cons(X,L)) >= Marked_mark(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(incr(X)) >= Marked_a__incr(mark(X)) ; Marked_mark(incr(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__incr(cons(X,L)) > Marked_mark(X) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(incr(X)) > Marked_a__incr(mark(X)) ; } { Marked_mark(incr(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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. === TIMER virtual : 50.000000 === trying sub matrices of size: 1 Matrix interpretation constraints generated. Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. Termination constraints generated. Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 50.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__incr(nil) >= nil constraint: a__incr(cons(X,L)) >= cons(s(mark(X)),incr(L)) constraint: a__incr(X) >= incr(X) constraint: mark(nil) >= nil constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(s(X)) >= s(mark(X)) constraint: mark(incr(X)) >= a__incr(mark(X)) constraint: mark(adx(X)) >= a__adx(mark(X)) constraint: mark(0) >= 0 constraint: mark(zeros) >= a__zeros constraint: mark(nats) >= a__nats constraint: mark(head(X)) >= a__head(mark(X)) constraint: mark(tail(X)) >= a__tail(mark(X)) constraint: a__adx(nil) >= nil constraint: a__adx(cons(X,L)) >= a__incr(cons(mark(X),adx(L))) constraint: a__adx(X) >= adx(X) constraint: a__zeros >= cons(0,zeros) constraint: a__zeros >= zeros constraint: a__nats >= a__adx(a__zeros) constraint: a__nats >= nats constraint: a__head(cons(X,L)) >= mark(X) constraint: a__head(X) >= head(X) constraint: a__tail(cons(X,L)) >= mark(L) constraint: a__tail(X) >= tail(X) constraint: Marked_a__incr(cons(X,L)) >= Marked_mark(X) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(incr(X)) >= Marked_a__incr(mark(X)) constraint: Marked_mark(incr(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_mark -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a__incr(nil) -> nil [2] a__incr(cons(X,L)) -> cons(s(mark(X)),incr(L)) [3] a__adx(nil) -> nil [4] a__adx(cons(X,L)) -> a__incr(cons(mark(X),adx(L))) [5] a__nats -> a__adx(a__zeros) [6] a__zeros -> cons(0,zeros) [7] a__head(cons(X,L)) -> mark(X) [8] a__tail(cons(X,L)) -> mark(L) [9] mark(incr(X)) -> a__incr(mark(X)) [10] mark(adx(X)) -> a__adx(mark(X)) [11] mark(nats) -> a__nats [12] mark(zeros) -> a__zeros [13] mark(head(X)) -> a__head(mark(X)) [14] mark(tail(X)) -> a__tail(mark(X)) [15] mark(nil) -> nil [16] mark(cons(X1,X2)) -> cons(mark(X1),X2) [17] mark(s(X)) -> s(mark(X)) [18] mark(0) -> 0 [19] a__incr(X) -> incr(X) [20] a__adx(X) -> adx(X) [21] a__nats -> nats [22] a__zeros -> zeros [23] a__head(X) -> head(X) [24] a__tail(X) -> tail(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: