- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(nil) -> nil [2] f(.(nil,y)) -> .(nil,f(y)) [3] f(.(.(x,y),z)) -> f(.(x,.(y,z))) [4] g(nil) -> nil [5] g(.(x,nil)) -> .(g(x),nil) [6] g(.(x,.(y,z))) -> g(.(.(x,y),z)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(nil) >= nil ; f(.(nil,y)) >= .(nil,f(y)) ; f(.(.(x,y),z)) >= f(.(x,.(y,z))) ; g(nil) >= nil ; g(.(x,nil)) >= .(g(x),nil) ; g(.(x,.(y,z))) >= g(.(.(x,y),z)) ; Marked_f(.(nil,y)) >= Marked_f(y) ; Marked_f(.(.(x,y),z)) >= Marked_f(.(x,.(y,z))) ; } + Disjunctions:{ { Marked_f(.(nil,y)) > Marked_f(y) ; } { Marked_f(.(.(x,y),z)) > Marked_f(.(x,.(y,z))) ; } } === 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: f(nil) >= nil constraint: f(.(nil,y)) >= .(nil,f(y)) constraint: f(.(.(x,y),z)) >= f(.(x,.(y,z))) constraint: g(nil) >= nil constraint: g(.(x,nil)) >= .(g(x),nil) constraint: g(.(x,.(y,z))) >= g(.(.(x,y),z)) constraint: Marked_f(.(nil,y)) >= Marked_f(y) constraint: Marked_f(.(.(x,y),z)) >= Marked_f(.(x,.(y,z))) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(nil) >= nil ; f(.(nil,y)) >= .(nil,f(y)) ; f(.(.(x,y),z)) >= f(.(x,.(y,z))) ; g(nil) >= nil ; g(.(x,nil)) >= .(g(x),nil) ; g(.(x,.(y,z))) >= g(.(.(x,y),z)) ; Marked_g(.(x,nil)) >= Marked_g(x) ; Marked_g(.(x,.(y,z))) >= Marked_g(.(.(x,y),z)) ; } + Disjunctions:{ { Marked_g(.(x,nil)) > Marked_g(x) ; } { Marked_g(.(x,.(y,z))) > Marked_g(.(.(x,y),z)) ; } } === 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: f(nil) >= nil constraint: f(.(nil,y)) >= .(nil,f(y)) constraint: f(.(.(x,y),z)) >= f(.(x,.(y,z))) constraint: g(nil) >= nil constraint: g(.(x,nil)) >= .(g(x),nil) constraint: g(.(x,.(y,z))) >= g(.(.(x,y),z)) constraint: Marked_g(.(x,nil)) >= Marked_g(x) constraint: Marked_g(.(x,.(y,z))) >= Marked_g(.(.(x,y),z)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(nil) >= nil ; f(.(nil,y)) >= .(nil,f(y)) ; f(.(.(x,y),z)) >= f(.(x,.(y,z))) ; g(nil) >= nil ; g(.(x,nil)) >= .(g(x),nil) ; g(.(x,.(y,z))) >= g(.(.(x,y),z)) ; Marked_f(.(.(x,y),z)) >= Marked_f(.(x,.(y,z))) ; } + Disjunctions:{ { Marked_f(.(.(x,y),z)) > Marked_f(.(x,.(y,z))) ; } } === 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 : 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: f(nil) >= nil constraint: f(.(nil,y)) >= .(nil,f(y)) constraint: f(.(.(x,y),z)) >= f(.(x,.(y,z))) constraint: g(nil) >= nil constraint: g(.(x,nil)) >= .(g(x),nil) constraint: g(.(x,.(y,z))) >= g(.(.(x,y),z)) constraint: Marked_f(.(.(x,y),z)) >= Marked_f(.(x,.(y,z))) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(nil) >= nil ; f(.(nil,y)) >= .(nil,f(y)) ; f(.(.(x,y),z)) >= f(.(x,.(y,z))) ; g(nil) >= nil ; g(.(x,nil)) >= .(g(x),nil) ; g(.(x,.(y,z))) >= g(.(.(x,y),z)) ; Marked_g(.(x,.(y,z))) >= Marked_g(.(.(x,y),z)) ; } + Disjunctions:{ { Marked_g(.(x,.(y,z))) > Marked_g(.(.(x,y),z)) ; } } === 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 : 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: f(nil) >= nil constraint: f(.(nil,y)) >= .(nil,f(y)) constraint: f(.(.(x,y),z)) >= f(.(x,.(y,z))) constraint: g(nil) >= nil constraint: g(.(x,nil)) >= .(g(x),nil) constraint: g(.(x,.(y,z))) >= g(.(.(x,y),z)) constraint: Marked_g(.(x,.(y,z))) >= Marked_g(.(.(x,y),z)) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(nil) -> nil [2] f(.(nil,y)) -> .(nil,f(y)) [3] f(.(.(x,y),z)) -> f(.(x,.(y,z))) [4] g(nil) -> nil [5] g(.(x,nil)) -> .(g(x),nil) [6] g(.(x,.(y,z))) -> g(.(.(x,y),z)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ nil ] () = 2; [ . ] (X0,X1) = 1*X1 + 1*X0; [ f ] (X0) = 2*X0; [ Marked_f ] (X0) = 1*X0; [ g ] (X0) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ nil ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ . ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ f ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_f ] (X0) = [ [ 1 , 0 , 0 ] [ 1 , 0 , 1 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ g ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} ]} ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ nil ] () = 1; [ Marked_g ] (X0) = 1*X0; [ . ] (X0,X1) = 1*X1 + 1*X0; [ f ] (X0) = 2*X0; [ g ] (X0) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ nil ] () = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_g ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ . ] (X0,X1) = [ [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ f ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 1 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ g ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} ]} ]} ]} ]} Cime worked for 1.706938 seconds (real time) Cime Exit Status: 0