- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a(h,h,h,x) -> s(x) [2] a(l,x,s(y),h) -> a(l,x,y,s(h)) [3] a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) [4] a(l,s(x),h,z) -> a(l,x,z,z) [5] a(s(l),h,h,z) -> a(l,z,h,z) [6] +(x,h) -> x [7] +(h,x) -> x [8] +(s(x),s(y)) -> s(s(+(x,y))) [9] +(+(x,y),z) -> +(x,+(y,z)) [10] s(h) -> 1 [11] app(nil,k) -> k [12] app(l,nil) -> l [13] app(cons(x,l),k) -> cons(x,app(l,k)) [14] sum(cons(x,nil)) -> cons(x,nil) [15] sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h,h),l)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> --> --> --> --> --> --> --> --> } { --> } { --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_+ -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_app -> 1 APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { s(h) >= 1 ; a(s(l),h,h,z) >= a(l,z,h,z) ; a(h,h,h,x) >= s(x) ; a(l,s(x),h,z) >= a(l,x,z,z) ; a(l,x,s(y),s(z)) >= a(l,x,y,a(l,x,s(y),z)) ; a(l,x,s(y),h) >= a(l,x,y,s(h)) ; +(s(x),s(y)) >= s(s(+(x,y))) ; +(h,x) >= x ; +(+(x,y),z) >= +(x,+(y,z)) ; +(x,h) >= x ; app(nil,k) >= k ; app(cons(x,l),k) >= cons(x,app(l,k)) ; app(l,nil) >= l ; sum(cons(x,nil)) >= cons(x,nil) ; sum(cons(x,cons(y,l))) >= sum(cons(a(x,y,h,h),l)) ; Marked_sum(cons(x,cons(y,l))) >= Marked_sum(cons(a(x,y,h,h),l)) ; } + Disjunctions:{ { Marked_sum(cons(x,cons(y,l))) > Marked_sum(cons(a(x,y,h,h),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: s(h) >= 1 constraint: a(s(l),h,h,z) >= a(l,z,h,z) constraint: a(h,h,h,x) >= s(x) constraint: a(l,s(x),h,z) >= a(l,x,z,z) constraint: a(l,x,s(y),s(z)) >= a(l,x,y,a(l,x,s(y),z)) constraint: a(l,x,s(y),h) >= a(l,x,y,s(h)) constraint: +(s(x),s(y)) >= s(s(+(x,y))) constraint: +(h,x) >= x constraint: +(+(x,y),z) >= +(x,+(y,z)) constraint: +(x,h) >= x constraint: app(nil,k) >= k constraint: app(cons(x,l),k) >= cons(x,app(l,k)) constraint: app(l,nil) >= l constraint: sum(cons(x,nil)) >= cons(x,nil) constraint: sum(cons(x,cons(y,l))) >= sum(cons(a(x,y,h,h),l)) constraint: Marked_sum(cons(x,cons(y,l))) >= Marked_sum(cons(a(x,y,h,h),l)) APPLY CRITERIA (Subterm criterion) ST: Marked_a -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_a -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_a -> 3 APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_a -> 4 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a(h,h,h,x) -> s(x) [2] a(l,x,s(y),h) -> a(l,x,y,s(h)) [3] a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) [4] a(l,s(x),h,z) -> a(l,x,z,z) [5] a(s(l),h,h,z) -> a(l,z,h,z) [6] +(x,h) -> x [7] +(h,x) -> x [8] +(s(x),s(y)) -> s(s(+(x,y))) [9] +(+(x,y),z) -> +(x,+(y,z)) [10] s(h) -> 1 [11] app(nil,k) -> k [12] app(l,nil) -> l [13] app(cons(x,l),k) -> cons(x,app(l,k)) [14] sum(cons(x,nil)) -> cons(x,nil) [15] sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h,h),l)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ s ] (X0) = 1*X0 + 0; [ sum ] (X0) = 2*X0 + 0; [ 1 ] () = 1 + 0; [ h ] () = 1 + 0; [ nil ] () = 0; [ a ] (X0,X1,X2,X3) = 1*X3 + 0; [ Marked_sum ] (X0) = 1*X0 + 0; [ app ] (X0,X1) = 1*X0 + 3*X1 + 0; [ + ] (X0,X1) = 1*X0 + 1*X1 + 0; [ cons ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} Cime worked for 0.102789 seconds (real time) Cime Exit Status: 0