/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: app(app(:(),app(app(:(),x),y)),z) -> app(app(:(),x),app(app(:(),y),z)) app(app(:(),app(app(+(),x),y)),z) -> app(app(+(),app(app(:(),x),z)),app(app(:(),y),z)) app(app(:(),z),app(app(+(),x),app(f,y))) -> app(app(:(),app(app(g(),z),y)),app(app(+(),x),a())) app(app(map(),f),nil()) -> nil() app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) app(app(filter(),f),nil()) -> nil() app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs) app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs)) app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs) Proof: DP Processor: DPs: app#(app(:(),app(app(:(),x),y)),z) -> app#(:(),y) app#(app(:(),app(app(:(),x),y)),z) -> app#(app(:(),y),z) app#(app(:(),app(app(:(),x),y)),z) -> app#(app(:(),x),app(app(:(),y),z)) app#(app(:(),app(app(+(),x),y)),z) -> app#(:(),y) app#(app(:(),app(app(+(),x),y)),z) -> app#(app(:(),y),z) app#(app(:(),app(app(+(),x),y)),z) -> app#(:(),x) app#(app(:(),app(app(+(),x),y)),z) -> app#(app(:(),x),z) app#(app(:(),app(app(+(),x),y)),z) -> app#(+(),app(app(:(),x),z)) app#(app(:(),app(app(+(),x),y)),z) -> app#(app(+(),app(app(:(),x),z)),app(app(:(),y),z)) app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(app(+(),x),a()) app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(g(),z) app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(app(g(),z),y) app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(:(),app(app(g(),z),y)) app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(app(:(),app(app(g(),z),y)),app(app(+(),x),a())) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(filter(),f) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(cons(),x),app(app(filter(),f),xs)) app#(app(app(app(filter2(),false()),f),x),xs) -> app#(filter(),f) app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) TRS: app(app(:(),app(app(:(),x),y)),z) -> app(app(:(),x),app(app(:(),y),z)) app(app(:(),app(app(+(),x),y)),z) -> app(app(+(),app(app(:(),x),z)),app(app(:(),y),z)) app(app(:(),z),app(app(+(),x),app(f,y))) -> app(app(:(),app(app(g(),z),y)),app(app(+(),x),a())) app(app(map(),f),nil()) -> nil() app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) app(app(filter(),f),nil()) -> nil() app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs) app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs)) app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs) EDG Processor: DPs: app#(app(:(),app(app(:(),x),y)),z) -> app#(:(),y) app#(app(:(),app(app(:(),x),y)),z) -> app#(app(:(),y),z) app#(app(:(),app(app(:(),x),y)),z) -> app#(app(:(),x),app(app(:(),y),z)) app#(app(:(),app(app(+(),x),y)),z) -> app#(:(),y) app#(app(:(),app(app(+(),x),y)),z) -> app#(app(:(),y),z) app#(app(:(),app(app(+(),x),y)),z) -> app#(:(),x) app#(app(:(),app(app(+(),x),y)),z) -> app#(app(:(),x),z) app#(app(:(),app(app(+(),x),y)),z) -> app#(+(),app(app(:(),x),z)) app#(app(:(),app(app(+(),x),y)),z) -> app#(app(+(),app(app(:(),x),z)),app(app(:(),y),z)) app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(app(+(),x),a()) app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(g(),z) app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(app(g(),z),y) app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(:(),app(app(g(),z),y)) app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(app(:(),app(app(g(),z),y)),app(app(+(),x),a())) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(filter(),f) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(cons(),x),app(app(filter(),f),xs)) app#(app(app(app(filter2(),false()),f),x),xs) -> app#(filter(),f) app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) TRS: app(app(:(),app(app(:(),x),y)),z) -> app(app(:(),x),app(app(:(),y),z)) app(app(:(),app(app(+(),x),y)),z) -> app(app(+(),app(app(:(),x),z)),app(app(:(),y),z)) app(app(:(),z),app(app(+(),x),app(f,y))) -> app(app(:(),app(app(g(),z),y)),app(app(+(),x),a())) app(app(map(),f),nil()) -> nil() app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) app(app(filter(),f),nil()) -> nil() app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs) app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs)) app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs) graph: app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),app(app(:(),x),y)),z) -> app#(:(),y) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),app(app(:(),x),y)),z) -> app#(app(:(),y),z) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),app(app(:(),x),y)),z) -> app#(app(:(),x),app(app(:(),y),z)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),app(app(+(),x),y)),z) -> app#(:(),y) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),app(app(+(),x),y)),z) -> app#(app(:(),y),z) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),app(app(+(),x),y)),z) -> app#(:(),x) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),app(app(+(),x),y)),z) -> app#(app(:(),x),z) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),app(app(+(),x),y)),z) -> app#(+(),app(app(:(),x),z)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),app(app(+(),x),y)),z) -> app#(app(+(),app(app(:(),x),z)),app(app(:(),y),z)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(app(+(),x),a()) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(g(),z) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(app(g(),z),y) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(:(),app(app(g(),z),y)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(app(:(),app(app(g(),z),y)),app(app(+(),x),a())) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(app(app(filter2(),true()),f),x),xs) -> app#(filter(),f) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(cons(),x),app(app(filter(),f),xs)) app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(app(app(filter2(),false()),f),x),xs) -> app#(filter(),f) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(:(),z),app(app(+(),x),app(f,y))) -> app#(app(+(),x),a()) app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x)) app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f) app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x) app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x)) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) -> app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs) app#(app(:(),app(app(:(),x),y)),z) -> app#(app(:(),y),z) -> app#(app(:(),app(app(+(),x),y)),z) -> app#(:(),y) SCC Processor: #sccs: 1 #rules: 2 #arcs: 40/841 DPs: app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) TRS: app(app(:(),app(app(:(),x),y)),z) -> app(app(:(),x),app(app(:(),y),z)) app(app(:(),app(app(+(),x),y)),z) -> app(app(+(),app(app(:(),x),z)),app(app(:(),y),z)) app(app(:(),z),app(app(+(),x),app(f,y))) -> app(app(:(),app(app(g(),z),y)),app(app(+(),x),a())) app(app(map(),f),nil()) -> nil() app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) app(app(filter(),f),nil()) -> nil() app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs) app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs)) app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs) Size-Change Termination Processor: DPs: TRS: app(app(:(),app(app(:(),x),y)),z) -> app(app(:(),x),app(app(:(),y),z)) app(app(:(),app(app(+(),x),y)),z) -> app(app(+(),app(app(:(),x),z)),app(app(:(),y),z)) app(app(:(),z),app(app(+(),x),app(f,y))) -> app(app(:(),app(app(g(),z),y)),app(app(+(),x),a())) app(app(map(),f),nil()) -> nil() app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) app(app(filter(),f),nil()) -> nil() app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs) app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs)) app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs) The DP: app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) has the edges: 0 > 0 1 > 1 The DP: app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) has the edges: 1 >= 1 Qed