/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: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Proof: DP Processor: DPs: a#(h(),h(),h(),x) -> s#(x) a#(l,x,s(y),h()) -> s#(h()) a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) a#(l,s(x),h(),z) -> a#(l,x,z,z) a#(s(l),h(),h(),z) -> a#(l,z,h(),z) +#(s(x),s(y)) -> +#(x,y) +#(s(x),s(y)) -> s#(+(x,y)) +#(s(x),s(y)) -> s#(s(+(x,y))) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) app#(cons(x,l),k) -> app#(l,k) sum#(cons(x,cons(y,l))) -> a#(x,y,h(),h()) sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h(),h()),l)) TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) TDG Processor: DPs: a#(h(),h(),h(),x) -> s#(x) a#(l,x,s(y),h()) -> s#(h()) a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) a#(l,s(x),h(),z) -> a#(l,x,z,z) a#(s(l),h(),h(),z) -> a#(l,z,h(),z) +#(s(x),s(y)) -> +#(x,y) +#(s(x),s(y)) -> s#(+(x,y)) +#(s(x),s(y)) -> s#(s(+(x,y))) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) app#(cons(x,l),k) -> app#(l,k) sum#(cons(x,cons(y,l))) -> a#(x,y,h(),h()) sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h(),h()),l)) TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) graph: sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h(),h()),l)) -> sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h(),h()),l)) sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h(),h()),l)) -> sum#(cons(x,cons(y,l))) -> a#(x,y,h(),h()) sum#(cons(x,cons(y,l))) -> a#(x,y,h(),h()) -> a#(s(l),h(),h(),z) -> a#(l,z,h(),z) sum#(cons(x,cons(y,l))) -> a#(x,y,h(),h()) -> a#(l,s(x),h(),z) -> a#(l,x,z,z) sum#(cons(x,cons(y,l))) -> a#(x,y,h(),h()) -> a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) sum#(cons(x,cons(y,l))) -> a#(x,y,h(),h()) -> a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) sum#(cons(x,cons(y,l))) -> a#(x,y,h(),h()) -> a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) sum#(cons(x,cons(y,l))) -> a#(x,y,h(),h()) -> a#(l,x,s(y),h()) -> s#(h()) sum#(cons(x,cons(y,l))) -> a#(x,y,h(),h()) -> a#(h(),h(),h(),x) -> s#(x) app#(cons(x,l),k) -> app#(l,k) -> app#(cons(x,l),k) -> app#(l,k) +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(y,z) -> +#(s(x),s(y)) -> s#(s(+(x,y))) +#(+(x,y),z) -> +#(y,z) -> +#(s(x),s(y)) -> s#(+(x,y)) +#(+(x,y),z) -> +#(y,z) -> +#(s(x),s(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(s(x),s(y)) -> s#(s(+(x,y))) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(s(x),s(y)) -> s#(+(x,y)) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(s(x),s(y)) -> +#(x,y) +#(s(x),s(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(s(x),s(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(s(x),s(y)) -> +#(x,y) -> +#(s(x),s(y)) -> s#(s(+(x,y))) +#(s(x),s(y)) -> +#(x,y) -> +#(s(x),s(y)) -> s#(+(x,y)) +#(s(x),s(y)) -> +#(x,y) -> +#(s(x),s(y)) -> +#(x,y) a#(s(l),h(),h(),z) -> a#(l,z,h(),z) -> a#(s(l),h(),h(),z) -> a#(l,z,h(),z) a#(s(l),h(),h(),z) -> a#(l,z,h(),z) -> a#(l,s(x),h(),z) -> a#(l,x,z,z) a#(s(l),h(),h(),z) -> a#(l,z,h(),z) -> a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) a#(s(l),h(),h(),z) -> a#(l,z,h(),z) -> a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) a#(s(l),h(),h(),z) -> a#(l,z,h(),z) -> a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) a#(s(l),h(),h(),z) -> a#(l,z,h(),z) -> a#(l,x,s(y),h()) -> s#(h()) 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#(s(l),h(),h(),z) -> a#(l,z,h(),z) a#(l,s(x),h(),z) -> a#(l,x,z,z) -> a#(l,s(x),h(),z) -> a#(l,x,z,z) 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,s(x),h(),z) -> a#(l,x,z,z) -> a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) a#(l,s(x),h(),z) -> a#(l,x,z,z) -> a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) a#(l,s(x),h(),z) -> a#(l,x,z,z) -> a#(l,x,s(y),h()) -> s#(h()) a#(l,s(x),h(),z) -> a#(l,x,z,z) -> a#(h(),h(),h(),x) -> s#(x) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) -> a#(s(l),h(),h(),z) -> a#(l,z,h(),z) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) -> a#(l,s(x),h(),z) -> a#(l,x,z,z) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) -> a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) -> a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) -> a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) -> a#(l,x,s(y),h()) -> s#(h()) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) -> a#(h(),h(),h(),x) -> s#(x) a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) -> a#(s(l),h(),h(),z) -> a#(l,z,h(),z) a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) -> 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),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) -> a#(l,x,s(y),s(z)) -> a#(l,x,s(y),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())) a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) -> a#(l,x,s(y),h()) -> s#(h()) a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) -> a#(h(),h(),h(),x) -> s#(x) a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) -> a#(s(l),h(),h(),z) -> a#(l,z,h(),z) a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) -> a#(l,s(x),h(),z) -> a#(l,x,z,z) a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) -> 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())) -> a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) -> a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) -> a#(l,x,s(y),h()) -> s#(h()) a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) -> a#(h(),h(),h(),x) -> s#(x) SCC Processor: #sccs: 4 #rules: 10 #arcs: 60/225 DPs: +#(+(x,y),z) -> +#(y,z) +#(s(x),s(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Subterm Criterion Processor: simple projection: pi(+#) = 0 problem: DPs: TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Qed DPs: app#(cons(x,l),k) -> app#(l,k) TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Subterm Criterion Processor: simple projection: pi(app#) = 0 problem: DPs: TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Qed DPs: sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h(),h()),l)) TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Subterm Criterion Processor: simple projection: pi(cons) = [1,1] pi(sum#) = [0,0] problem: DPs: TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Qed DPs: a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) a#(l,s(x),h(),z) -> a#(l,x,z,z) a#(s(l),h(),h(),z) -> a#(l,z,h(),z) TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Subterm Criterion Processor: simple projection: pi(a#) = 0 problem: DPs: a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) a#(l,s(x),h(),z) -> a#(l,x,z,z) TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Subterm Criterion Processor: simple projection: pi(a#) = 1 problem: DPs: a#(l,x,s(y),h()) -> a#(l,x,y,s(h())) a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) a#(l,x,s(y),s(z)) -> a#(l,x,y,a(l,x,s(y),z)) TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Subterm Criterion Processor: simple projection: pi(a#) = 2 problem: DPs: a#(l,x,s(y),s(z)) -> a#(l,x,s(y),z) TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Subterm Criterion Processor: simple projection: pi(a#) = 3 problem: DPs: TRS: a(h(),h(),h(),x) -> s(x) a(l,x,s(y),h()) -> a(l,x,y,s(h())) a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z)) a(l,s(x),h(),z) -> a(l,x,z,z) a(s(l),h(),h(),z) -> a(l,z,h(),z) +(x,h()) -> x +(h(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) s(h()) -> 1() app(nil(),k) -> k app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) sum(cons(x,nil())) -> cons(x,nil()) sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l)) Qed