/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) 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)) *#(s(x),s(y)) -> *#(x,y) *#(s(x),s(y)) -> +#(*(x,y),x) *#(s(x),s(y)) -> +#(+(*(x,y),x),y) *#(s(x),s(y)) -> s#(+(+(*(x,y),x),y)) 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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) 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)) *#(s(x),s(y)) -> *#(x,y) *#(s(x),s(y)) -> +#(*(x,y),x) *#(s(x),s(y)) -> +#(+(*(x,y),x),y) *#(s(x),s(y)) -> s#(+(+(*(x,y),x),y)) 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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) graph: *#(s(x),s(y)) -> *#(x,y) -> *#(s(x),s(y)) -> s#(+(+(*(x,y),x),y)) *#(s(x),s(y)) -> *#(x,y) -> *#(s(x),s(y)) -> +#(+(*(x,y),x),y) *#(s(x),s(y)) -> *#(x,y) -> *#(s(x),s(y)) -> +#(*(x,y),x) *#(s(x),s(y)) -> *#(x,y) -> *#(s(x),s(y)) -> *#(x,y) *#(s(x),s(y)) -> +#(*(x,y),x) -> +#(+(x,y),z) -> +#(x,+(y,z)) *#(s(x),s(y)) -> +#(*(x,y),x) -> +#(+(x,y),z) -> +#(y,z) *#(s(x),s(y)) -> +#(*(x,y),x) -> +#(s(x),s(y)) -> s#(s(+(x,y))) *#(s(x),s(y)) -> +#(*(x,y),x) -> +#(s(x),s(y)) -> s#(+(x,y)) *#(s(x),s(y)) -> +#(*(x,y),x) -> +#(s(x),s(y)) -> +#(x,y) *#(s(x),s(y)) -> +#(+(*(x,y),x),y) -> +#(+(x,y),z) -> +#(x,+(y,z)) *#(s(x),s(y)) -> +#(+(*(x,y),x),y) -> +#(+(x,y),z) -> +#(y,z) *#(s(x),s(y)) -> +#(+(*(x,y),x),y) -> +#(s(x),s(y)) -> s#(s(+(x,y))) *#(s(x),s(y)) -> +#(+(*(x,y),x),y) -> +#(s(x),s(y)) -> s#(+(x,y)) *#(s(x),s(y)) -> +#(+(*(x,y),x),y) -> +#(s(x),s(y)) -> +#(x,y) +#(+(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: 3 #rules: 9 #arcs: 64/256 DPs: 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,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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) 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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) 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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) 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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) 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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) Qed DPs: *#(s(x),s(y)) -> *#(x,y) 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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) 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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) Qed DPs: +#(s(x),s(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) +#(+(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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) 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() *(h(),x) -> h() *(x,h()) -> h() *(s(x),s(y)) -> s(+(+(*(x,y),x),y)) Qed