/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: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) Proof: DP Processor: DPs: +#(0(x),0(y)) -> +#(x,y) +#(0(x),0(y)) -> 0#(+(x,y)) +#(0(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),j(y)) -> +#(x,y) +#(1(x),j(y)) -> 0#(+(x,y)) +#(j(x),1(y)) -> +#(x,y) +#(j(x),1(y)) -> 0#(+(x,y)) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) opp#(0(x)) -> opp#(x) opp#(0(x)) -> 0#(opp(x)) opp#(1(x)) -> opp#(x) opp#(j(x)) -> opp#(x) -#(x,y) -> opp#(y) -#(x,y) -> +#(x,opp(y)) *#(0(x),y) -> *#(x,y) *#(0(x),y) -> 0#(*(x,y)) *#(1(x),y) -> *#(x,y) *#(1(x),y) -> 0#(*(x,y)) *#(1(x),y) -> +#(0(*(x,y)),y) *#(j(x),y) -> *#(x,y) *#(j(x),y) -> 0#(*(x,y)) *#(j(x),y) -> -#(0(*(x,y)),y) *#(*(x,y),z) -> *#(y,z) *#(*(x,y),z) -> *#(x,*(y,z)) *#(+(x,y),z) -> *#(y,z) *#(+(x,y),z) -> *#(x,z) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(x,+(y,z)) -> *#(x,z) *#(x,+(y,z)) -> *#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) TDG Processor: DPs: +#(0(x),0(y)) -> +#(x,y) +#(0(x),0(y)) -> 0#(+(x,y)) +#(0(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),j(y)) -> +#(x,y) +#(1(x),j(y)) -> 0#(+(x,y)) +#(j(x),1(y)) -> +#(x,y) +#(j(x),1(y)) -> 0#(+(x,y)) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) opp#(0(x)) -> opp#(x) opp#(0(x)) -> 0#(opp(x)) opp#(1(x)) -> opp#(x) opp#(j(x)) -> opp#(x) -#(x,y) -> opp#(y) -#(x,y) -> +#(x,opp(y)) *#(0(x),y) -> *#(x,y) *#(0(x),y) -> 0#(*(x,y)) *#(1(x),y) -> *#(x,y) *#(1(x),y) -> 0#(*(x,y)) *#(1(x),y) -> +#(0(*(x,y)),y) *#(j(x),y) -> *#(x,y) *#(j(x),y) -> 0#(*(x,y)) *#(j(x),y) -> -#(0(*(x,y)),y) *#(*(x,y),z) -> *#(y,z) *#(*(x,y),z) -> *#(x,*(y,z)) *#(+(x,y),z) -> *#(y,z) *#(+(x,y),z) -> *#(x,z) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(x,+(y,z)) -> *#(x,z) *#(x,+(y,z)) -> *#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) graph: *#(*(x,y),z) -> *#(y,z) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) *#(*(x,y),z) -> *#(y,z) -> *#(x,+(y,z)) -> *#(x,y) *#(*(x,y),z) -> *#(y,z) -> *#(x,+(y,z)) -> *#(x,z) *#(*(x,y),z) -> *#(y,z) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(*(x,y),z) -> *#(y,z) -> *#(+(x,y),z) -> *#(x,z) *#(*(x,y),z) -> *#(y,z) -> *#(+(x,y),z) -> *#(y,z) *#(*(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) -> *#(j(x),y) -> -#(0(*(x,y)),y) *#(*(x,y),z) -> *#(y,z) -> *#(j(x),y) -> 0#(*(x,y)) *#(*(x,y),z) -> *#(y,z) -> *#(j(x),y) -> *#(x,y) *#(*(x,y),z) -> *#(y,z) -> *#(1(x),y) -> +#(0(*(x,y)),y) *#(*(x,y),z) -> *#(y,z) -> *#(1(x),y) -> 0#(*(x,y)) *#(*(x,y),z) -> *#(y,z) -> *#(1(x),y) -> *#(x,y) *#(*(x,y),z) -> *#(y,z) -> *#(0(x),y) -> 0#(*(x,y)) *#(*(x,y),z) -> *#(y,z) -> *#(0(x),y) -> *#(x,y) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(x,+(y,z)) -> *#(x,y) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(x,+(y,z)) -> *#(x,z) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(+(x,y),z) -> *#(x,z) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(+(x,y),z) -> *#(y,z) *#(*(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)) -> *#(j(x),y) -> -#(0(*(x,y)),y) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(j(x),y) -> 0#(*(x,y)) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(j(x),y) -> *#(x,y) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(1(x),y) -> +#(0(*(x,y)),y) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(1(x),y) -> 0#(*(x,y)) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(1(x),y) -> *#(x,y) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(0(x),y) -> 0#(*(x,y)) *#(*(x,y),z) -> *#(x,*(y,z)) -> *#(0(x),y) -> *#(x,y) *#(j(x),y) -> *#(x,y) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) *#(j(x),y) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,y) *#(j(x),y) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,z) *#(j(x),y) -> *#(x,y) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(j(x),y) -> *#(x,y) -> *#(+(x,y),z) -> *#(x,z) *#(j(x),y) -> *#(x,y) -> *#(+(x,y),z) -> *#(y,z) *#(j(x),y) -> *#(x,y) -> *#(*(x,y),z) -> *#(x,*(y,z)) *#(j(x),y) -> *#(x,y) -> *#(*(x,y),z) -> *#(y,z) *#(j(x),y) -> *#(x,y) -> *#(j(x),y) -> -#(0(*(x,y)),y) *#(j(x),y) -> *#(x,y) -> *#(j(x),y) -> 0#(*(x,y)) *#(j(x),y) -> *#(x,y) -> *#(j(x),y) -> *#(x,y) *#(j(x),y) -> *#(x,y) -> *#(1(x),y) -> +#(0(*(x,y)),y) *#(j(x),y) -> *#(x,y) -> *#(1(x),y) -> 0#(*(x,y)) *#(j(x),y) -> *#(x,y) -> *#(1(x),y) -> *#(x,y) *#(j(x),y) -> *#(x,y) -> *#(0(x),y) -> 0#(*(x,y)) *#(j(x),y) -> *#(x,y) -> *#(0(x),y) -> *#(x,y) *#(j(x),y) -> -#(0(*(x,y)),y) -> -#(x,y) -> +#(x,opp(y)) *#(j(x),y) -> -#(0(*(x,y)),y) -> -#(x,y) -> opp#(y) *#(1(x),y) -> *#(x,y) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) *#(1(x),y) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,y) *#(1(x),y) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,z) *#(1(x),y) -> *#(x,y) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(1(x),y) -> *#(x,y) -> *#(+(x,y),z) -> *#(x,z) *#(1(x),y) -> *#(x,y) -> *#(+(x,y),z) -> *#(y,z) *#(1(x),y) -> *#(x,y) -> *#(*(x,y),z) -> *#(x,*(y,z)) *#(1(x),y) -> *#(x,y) -> *#(*(x,y),z) -> *#(y,z) *#(1(x),y) -> *#(x,y) -> *#(j(x),y) -> -#(0(*(x,y)),y) *#(1(x),y) -> *#(x,y) -> *#(j(x),y) -> 0#(*(x,y)) *#(1(x),y) -> *#(x,y) -> *#(j(x),y) -> *#(x,y) *#(1(x),y) -> *#(x,y) -> *#(1(x),y) -> +#(0(*(x,y)),y) *#(1(x),y) -> *#(x,y) -> *#(1(x),y) -> 0#(*(x,y)) *#(1(x),y) -> *#(x,y) -> *#(1(x),y) -> *#(x,y) *#(1(x),y) -> *#(x,y) -> *#(0(x),y) -> 0#(*(x,y)) *#(1(x),y) -> *#(x,y) -> *#(0(x),y) -> *#(x,y) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(+(x,y),z) -> +#(x,+(y,z)) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(+(x,y),z) -> +#(y,z) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(j(x),1(y)) -> 0#(+(x,y)) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(j(x),1(y)) -> +#(x,y) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(1(x),j(y)) -> 0#(+(x,y)) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(1(x),j(y)) -> +#(x,y) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(j(x),j(y)) -> +#(x,y) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(1(x),1(y)) -> +#(x,y) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(j(x),0(y)) -> +#(x,y) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(0(x),j(y)) -> +#(x,y) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(1(x),0(y)) -> +#(x,y) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(0(x),1(y)) -> +#(x,y) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(0(x),0(y)) -> 0#(+(x,y)) *#(1(x),y) -> +#(0(*(x,y)),y) -> +#(0(x),0(y)) -> +#(x,y) *#(+(x,y),z) -> *#(y,z) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) *#(+(x,y),z) -> *#(y,z) -> *#(x,+(y,z)) -> *#(x,y) *#(+(x,y),z) -> *#(y,z) -> *#(x,+(y,z)) -> *#(x,z) *#(+(x,y),z) -> *#(y,z) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(+(x,y),z) -> *#(y,z) -> *#(+(x,y),z) -> *#(x,z) *#(+(x,y),z) -> *#(y,z) -> *#(+(x,y),z) -> *#(y,z) *#(+(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) -> *#(j(x),y) -> -#(0(*(x,y)),y) *#(+(x,y),z) -> *#(y,z) -> *#(j(x),y) -> 0#(*(x,y)) *#(+(x,y),z) -> *#(y,z) -> *#(j(x),y) -> *#(x,y) *#(+(x,y),z) -> *#(y,z) -> *#(1(x),y) -> +#(0(*(x,y)),y) *#(+(x,y),z) -> *#(y,z) -> *#(1(x),y) -> 0#(*(x,y)) *#(+(x,y),z) -> *#(y,z) -> *#(1(x),y) -> *#(x,y) *#(+(x,y),z) -> *#(y,z) -> *#(0(x),y) -> 0#(*(x,y)) *#(+(x,y),z) -> *#(y,z) -> *#(0(x),y) -> *#(x,y) *#(+(x,y),z) -> *#(x,z) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) *#(+(x,y),z) -> *#(x,z) -> *#(x,+(y,z)) -> *#(x,y) *#(+(x,y),z) -> *#(x,z) -> *#(x,+(y,z)) -> *#(x,z) *#(+(x,y),z) -> *#(x,z) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(+(x,y),z) -> *#(x,z) -> *#(+(x,y),z) -> *#(x,z) *#(+(x,y),z) -> *#(x,z) -> *#(+(x,y),z) -> *#(y,z) *#(+(x,y),z) -> *#(x,z) -> *#(*(x,y),z) -> *#(x,*(y,z)) *#(+(x,y),z) -> *#(x,z) -> *#(*(x,y),z) -> *#(y,z) *#(+(x,y),z) -> *#(x,z) -> *#(j(x),y) -> -#(0(*(x,y)),y) *#(+(x,y),z) -> *#(x,z) -> *#(j(x),y) -> 0#(*(x,y)) *#(+(x,y),z) -> *#(x,z) -> *#(j(x),y) -> *#(x,y) *#(+(x,y),z) -> *#(x,z) -> *#(1(x),y) -> +#(0(*(x,y)),y) *#(+(x,y),z) -> *#(x,z) -> *#(1(x),y) -> 0#(*(x,y)) *#(+(x,y),z) -> *#(x,z) -> *#(1(x),y) -> *#(x,y) *#(+(x,y),z) -> *#(x,z) -> *#(0(x),y) -> 0#(*(x,y)) *#(+(x,y),z) -> *#(x,z) -> *#(0(x),y) -> *#(x,y) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(+(x,y),z) -> +#(y,z) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(j(x),1(y)) -> 0#(+(x,y)) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(j(x),1(y)) -> +#(x,y) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(1(x),j(y)) -> 0#(+(x,y)) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(1(x),j(y)) -> +#(x,y) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(j(x),j(y)) -> +#(x,y) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(1(x),1(y)) -> +#(x,y) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(j(x),0(y)) -> +#(x,y) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(0(x),j(y)) -> +#(x,y) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(1(x),0(y)) -> +#(x,y) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(0(x),1(y)) -> +#(x,y) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(0(x),0(y)) -> 0#(+(x,y)) *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(0(x),0(y)) -> +#(x,y) *#(0(x),y) -> *#(x,y) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) *#(0(x),y) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,y) *#(0(x),y) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,z) *#(0(x),y) -> *#(x,y) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(0(x),y) -> *#(x,y) -> *#(+(x,y),z) -> *#(x,z) *#(0(x),y) -> *#(x,y) -> *#(+(x,y),z) -> *#(y,z) *#(0(x),y) -> *#(x,y) -> *#(*(x,y),z) -> *#(x,*(y,z)) *#(0(x),y) -> *#(x,y) -> *#(*(x,y),z) -> *#(y,z) *#(0(x),y) -> *#(x,y) -> *#(j(x),y) -> -#(0(*(x,y)),y) *#(0(x),y) -> *#(x,y) -> *#(j(x),y) -> 0#(*(x,y)) *#(0(x),y) -> *#(x,y) -> *#(j(x),y) -> *#(x,y) *#(0(x),y) -> *#(x,y) -> *#(1(x),y) -> +#(0(*(x,y)),y) *#(0(x),y) -> *#(x,y) -> *#(1(x),y) -> 0#(*(x,y)) *#(0(x),y) -> *#(x,y) -> *#(1(x),y) -> *#(x,y) *#(0(x),y) -> *#(x,y) -> *#(0(x),y) -> 0#(*(x,y)) *#(0(x),y) -> *#(x,y) -> *#(0(x),y) -> *#(x,y) *#(x,+(y,z)) -> *#(x,z) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) *#(x,+(y,z)) -> *#(x,z) -> *#(x,+(y,z)) -> *#(x,y) *#(x,+(y,z)) -> *#(x,z) -> *#(x,+(y,z)) -> *#(x,z) *#(x,+(y,z)) -> *#(x,z) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(x,+(y,z)) -> *#(x,z) -> *#(+(x,y),z) -> *#(x,z) *#(x,+(y,z)) -> *#(x,z) -> *#(+(x,y),z) -> *#(y,z) *#(x,+(y,z)) -> *#(x,z) -> *#(*(x,y),z) -> *#(x,*(y,z)) *#(x,+(y,z)) -> *#(x,z) -> *#(*(x,y),z) -> *#(y,z) *#(x,+(y,z)) -> *#(x,z) -> *#(j(x),y) -> -#(0(*(x,y)),y) *#(x,+(y,z)) -> *#(x,z) -> *#(j(x),y) -> 0#(*(x,y)) *#(x,+(y,z)) -> *#(x,z) -> *#(j(x),y) -> *#(x,y) *#(x,+(y,z)) -> *#(x,z) -> *#(1(x),y) -> +#(0(*(x,y)),y) *#(x,+(y,z)) -> *#(x,z) -> *#(1(x),y) -> 0#(*(x,y)) *#(x,+(y,z)) -> *#(x,z) -> *#(1(x),y) -> *#(x,y) *#(x,+(y,z)) -> *#(x,z) -> *#(0(x),y) -> 0#(*(x,y)) *#(x,+(y,z)) -> *#(x,z) -> *#(0(x),y) -> *#(x,y) *#(x,+(y,z)) -> *#(x,y) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) *#(x,+(y,z)) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,y) *#(x,+(y,z)) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,z) *#(x,+(y,z)) -> *#(x,y) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z)) *#(x,+(y,z)) -> *#(x,y) -> *#(+(x,y),z) -> *#(x,z) *#(x,+(y,z)) -> *#(x,y) -> *#(+(x,y),z) -> *#(y,z) *#(x,+(y,z)) -> *#(x,y) -> *#(*(x,y),z) -> *#(x,*(y,z)) *#(x,+(y,z)) -> *#(x,y) -> *#(*(x,y),z) -> *#(y,z) *#(x,+(y,z)) -> *#(x,y) -> *#(j(x),y) -> -#(0(*(x,y)),y) *#(x,+(y,z)) -> *#(x,y) -> *#(j(x),y) -> 0#(*(x,y)) *#(x,+(y,z)) -> *#(x,y) -> *#(j(x),y) -> *#(x,y) *#(x,+(y,z)) -> *#(x,y) -> *#(1(x),y) -> +#(0(*(x,y)),y) *#(x,+(y,z)) -> *#(x,y) -> *#(1(x),y) -> 0#(*(x,y)) *#(x,+(y,z)) -> *#(x,y) -> *#(1(x),y) -> *#(x,y) *#(x,+(y,z)) -> *#(x,y) -> *#(0(x),y) -> 0#(*(x,y)) *#(x,+(y,z)) -> *#(x,y) -> *#(0(x),y) -> *#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(+(x,y),z) -> +#(y,z) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(j(x),1(y)) -> 0#(+(x,y)) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(j(x),1(y)) -> +#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(1(x),j(y)) -> 0#(+(x,y)) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(1(x),j(y)) -> +#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(j(x),j(y)) -> +#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(1(x),1(y)) -> +#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(j(x),0(y)) -> +#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(0(x),j(y)) -> +#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(1(x),0(y)) -> +#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(0(x),1(y)) -> +#(x,y) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(0(x),0(y)) -> 0#(+(x,y)) *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(0(x),0(y)) -> +#(x,y) -#(x,y) -> opp#(y) -> opp#(j(x)) -> opp#(x) -#(x,y) -> opp#(y) -> opp#(1(x)) -> opp#(x) -#(x,y) -> opp#(y) -> opp#(0(x)) -> 0#(opp(x)) -#(x,y) -> opp#(y) -> opp#(0(x)) -> opp#(x) -#(x,y) -> +#(x,opp(y)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -#(x,y) -> +#(x,opp(y)) -> +#(+(x,y),z) -> +#(y,z) -#(x,y) -> +#(x,opp(y)) -> +#(j(x),1(y)) -> 0#(+(x,y)) -#(x,y) -> +#(x,opp(y)) -> +#(j(x),1(y)) -> +#(x,y) -#(x,y) -> +#(x,opp(y)) -> +#(1(x),j(y)) -> 0#(+(x,y)) -#(x,y) -> +#(x,opp(y)) -> +#(1(x),j(y)) -> +#(x,y) -#(x,y) -> +#(x,opp(y)) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) -#(x,y) -> +#(x,opp(y)) -> +#(j(x),j(y)) -> +#(x,y) -#(x,y) -> +#(x,opp(y)) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) -#(x,y) -> +#(x,opp(y)) -> +#(1(x),1(y)) -> +#(x,y) -#(x,y) -> +#(x,opp(y)) -> +#(j(x),0(y)) -> +#(x,y) -#(x,y) -> +#(x,opp(y)) -> +#(0(x),j(y)) -> +#(x,y) -#(x,y) -> +#(x,opp(y)) -> +#(1(x),0(y)) -> +#(x,y) -#(x,y) -> +#(x,opp(y)) -> +#(0(x),1(y)) -> +#(x,y) -#(x,y) -> +#(x,opp(y)) -> +#(0(x),0(y)) -> 0#(+(x,y)) -#(x,y) -> +#(x,opp(y)) -> +#(0(x),0(y)) -> +#(x,y) opp#(j(x)) -> opp#(x) -> opp#(j(x)) -> opp#(x) opp#(j(x)) -> opp#(x) -> opp#(1(x)) -> opp#(x) opp#(j(x)) -> opp#(x) -> opp#(0(x)) -> 0#(opp(x)) opp#(j(x)) -> opp#(x) -> opp#(0(x)) -> opp#(x) opp#(1(x)) -> opp#(x) -> opp#(j(x)) -> opp#(x) opp#(1(x)) -> opp#(x) -> opp#(1(x)) -> opp#(x) opp#(1(x)) -> opp#(x) -> opp#(0(x)) -> 0#(opp(x)) opp#(1(x)) -> opp#(x) -> opp#(0(x)) -> opp#(x) opp#(0(x)) -> opp#(x) -> opp#(j(x)) -> opp#(x) opp#(0(x)) -> opp#(x) -> opp#(1(x)) -> opp#(x) opp#(0(x)) -> opp#(x) -> opp#(0(x)) -> 0#(opp(x)) opp#(0(x)) -> opp#(x) -> opp#(0(x)) -> opp#(x) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(+(x,y),z) -> +#(y,z) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(j(x),1(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(1(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(j(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(1(x),1(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(j(x),0(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(0(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(1(x),0(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(0(x),1(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(0(x),0(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(j(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(j(x),j(y)) -> +#(x,y) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(j(x),j(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(j(x),j(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(j(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(j(x),j(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(j(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(j(x),1(y)) -> +#(x,y) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(j(x),1(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(j(x),1(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(j(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(j(x),1(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(j(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(j(x),0(y)) -> +#(x,y) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(j(x),0(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(j(x),0(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(j(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(j(x),0(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(1(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(1(x),j(y)) -> +#(x,y) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(1(x),j(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(1(x),j(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(1(x),j(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(+(x,y),z) -> +#(y,z) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(j(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(1(x),j(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(j(x),j(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(j(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(0(x),j(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(1(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(0(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(0(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(1(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(1(x),1(y)) -> +#(x,y) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(1(x),1(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(1(x),1(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(1(x),1(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(1(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(1(x),0(y)) -> +#(x,y) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(1(x),0(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(1(x),0(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(1(x),0(y)) -> +#(x,y) -> +#(0(x),0(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) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(+(x,y),z) -> +#(y,z) -> +#(j(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(+(x,y),z) -> +#(y,z) -> +#(1(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(+(x,y),z) -> +#(y,z) -> +#(j(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(+(x,y),z) -> +#(y,z) -> +#(1(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(j(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(0(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(1(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(0(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(+(x,y),z) -> +#(y,z) -> +#(0(x),0(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)) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(j(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(1(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(j(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(1(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(j(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(0(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(1(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(0(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(0(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(0(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(0(x),j(y)) -> +#(x,y) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(0(x),j(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(0(x),j(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(0(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(0(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(0(x),j(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(0(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(0(x),1(y)) -> +#(x,y) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(0(x),1(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(0(x),1(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(0(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(0(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(0(x),1(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(0(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(0(x),0(y)) -> +#(x,y) -> +#(j(x),1(y)) -> 0#(+(x,y)) +#(0(x),0(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(1(x),j(y)) -> 0#(+(x,y)) +#(0(x),0(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(0(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(0(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(0(x),0(y)) -> 0#(+(x,y)) +#(0(x),0(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) SCC Processor: #sccs: 3 #rules: 25 #arcs: 434/1444 DPs: *#(*(x,y),z) -> *#(y,z) *#(0(x),y) -> *#(x,y) *#(1(x),y) -> *#(x,y) *#(j(x),y) -> *#(x,y) *#(*(x,y),z) -> *#(x,*(y,z)) *#(+(x,y),z) -> *#(y,z) *#(+(x,y),z) -> *#(x,z) *#(x,+(y,z)) -> *#(x,z) *#(x,+(y,z)) -> *#(x,y) TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) Subterm Criterion Processor: simple projection: pi(*#) = 0 problem: DPs: *#(x,+(y,z)) -> *#(x,z) *#(x,+(y,z)) -> *#(x,y) TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) Subterm Criterion Processor: simple projection: pi(*#) = 1 problem: DPs: TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) Qed DPs: opp#(0(x)) -> opp#(x) opp#(1(x)) -> opp#(x) opp#(j(x)) -> opp#(x) TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) Subterm Criterion Processor: simple projection: pi(opp#) = 0 problem: DPs: TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) Qed DPs: +#(0(x),0(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),j(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) EDG Processor: DPs: +#(0(x),0(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),j(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) graph: +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(0(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(j(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(1(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(+(x,y),z) -> +#(y,z) +#(j(x),j(y)) -> +#(+(x,y),j(#())) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(j(x),j(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(j(x),j(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(j(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(j(x),1(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(j(x),1(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(j(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(j(x),0(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(j(x),0(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(j(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(1(x),j(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),j(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(1(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(1(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(0(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(j(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(+(x,y),z) -> +#(y,z) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(1(x),1(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),1(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(1(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(1(x),0(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),0(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(1(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(+(x,y),z) -> +#(y,z) -> +#(0(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(0(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(1(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(0(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(j(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(1(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(+(x,y),z) -> +#(y,z) -> +#(j(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(+(x,y),z) -> +#(y,z) -> +#(1(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(j(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(0(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(0(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(1(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(0(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(j(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(1(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(j(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(1(x),j(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(j(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(0(x),j(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(0(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(0(x),j(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(0(x),j(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(0(x),1(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(0(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(0(x),1(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(0(x),1(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(0(x),0(y)) -> +#(x,y) -> +#(0(x),0(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(0(x),1(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(1(x),0(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(0(x),j(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(j(x),0(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(0(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(0(x),0(y)) -> +#(x,y) -> +#(1(x),j(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(j(x),1(y)) -> +#(x,y) +#(0(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(y,z) +#(0(x),0(y)) -> +#(x,y) -> +#(+(x,y),z) -> +#(x,+(y,z)) Usable Rule Processor: DPs: +#(0(x),0(y)) -> +#(x,y) +#(0(x),1(y)) -> +#(x,y) +#(1(x),0(y)) -> +#(x,y) +#(0(x),j(y)) -> +#(x,y) +#(j(x),0(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(j(x),j(y)) -> +#(x,y) +#(j(x),j(y)) -> +#(+(x,y),j(#())) +#(1(x),j(y)) -> +#(x,y) +#(j(x),1(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) TRS: +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) 0(#()) -> #() Matrix Interpretation Processor: dim=1 usable rules: +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) 0(#()) -> #() interpretation: [+#](x0, x1) = 4x0 + 4x1, [j](x0) = x0 + 1, [1](x0) = x0 + 1, [+](x0, x1) = x0 + x1, [0](x0) = x0, [#] = 0 orientation: +#(0(x),0(y)) = 4x + 4y >= 4x + 4y = +#(x,y) +#(0(x),1(y)) = 4x + 4y + 4 >= 4x + 4y = +#(x,y) +#(1(x),0(y)) = 4x + 4y + 4 >= 4x + 4y = +#(x,y) +#(0(x),j(y)) = 4x + 4y + 4 >= 4x + 4y = +#(x,y) +#(j(x),0(y)) = 4x + 4y + 4 >= 4x + 4y = +#(x,y) +#(1(x),1(y)) = 4x + 4y + 8 >= 4x + 4y = +#(x,y) +#(1(x),1(y)) = 4x + 4y + 8 >= 4x + 4y + 4 = +#(+(x,y),1(#())) +#(j(x),j(y)) = 4x + 4y + 8 >= 4x + 4y = +#(x,y) +#(j(x),j(y)) = 4x + 4y + 8 >= 4x + 4y + 4 = +#(+(x,y),j(#())) +#(1(x),j(y)) = 4x + 4y + 8 >= 4x + 4y = +#(x,y) +#(j(x),1(y)) = 4x + 4y + 8 >= 4x + 4y = +#(x,y) +#(+(x,y),z) = 4x + 4y + 4z >= 4y + 4z = +#(y,z) +#(+(x,y),z) = 4x + 4y + 4z >= 4x + 4y + 4z = +#(x,+(y,z)) +(#(),x) = x >= x = x +(x,#()) = x >= x = x +(0(x),0(y)) = x + y >= x + y = 0(+(x,y)) +(0(x),1(y)) = x + y + 1 >= x + y + 1 = 1(+(x,y)) +(1(x),0(y)) = x + y + 1 >= x + y + 1 = 1(+(x,y)) +(0(x),j(y)) = x + y + 1 >= x + y + 1 = j(+(x,y)) +(j(x),0(y)) = x + y + 1 >= x + y + 1 = j(+(x,y)) +(1(x),1(y)) = x + y + 2 >= x + y + 2 = j(+(+(x,y),1(#()))) +(j(x),j(y)) = x + y + 2 >= x + y + 2 = 1(+(+(x,y),j(#()))) +(1(x),j(y)) = x + y + 2 >= x + y = 0(+(x,y)) +(j(x),1(y)) = x + y + 2 >= x + y = 0(+(x,y)) +(+(x,y),z) = x + y + z >= x + y + z = +(x,+(y,z)) 0(#()) = 0 >= 0 = #() problem: DPs: +#(0(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) TRS: +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) 0(#()) -> #() Restore Modifier: DPs: +#(0(x),0(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) Size-Change Termination Processor: DPs: TRS: 0(#()) -> #() +(#(),x) -> x +(x,#()) -> x +(0(x),0(y)) -> 0(+(x,y)) +(0(x),1(y)) -> 1(+(x,y)) +(1(x),0(y)) -> 1(+(x,y)) +(0(x),j(y)) -> j(+(x,y)) +(j(x),0(y)) -> j(+(x,y)) +(1(x),1(y)) -> j(+(+(x,y),1(#()))) +(j(x),j(y)) -> 1(+(+(x,y),j(#()))) +(1(x),j(y)) -> 0(+(x,y)) +(j(x),1(y)) -> 0(+(x,y)) +(+(x,y),z) -> +(x,+(y,z)) opp(#()) -> #() opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) -(x,y) -> +(x,opp(y)) *(#(),x) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) *(j(x),y) -> -(0(*(x,y)),y) *(*(x,y),z) -> *(x,*(y,z)) *(+(x,y),z) -> +(*(x,z),*(y,z)) *(x,+(y,z)) -> +(*(x,y),*(x,z)) The DP: +#(0(x),0(y)) -> +#(x,y) has the edges: 0 > 0 1 > 1 The DP: +#(+(x,y),z) -> +#(y,z) has the edges: 0 > 0 1 >= 1 The DP: +#(+(x,y),z) -> +#(x,+(y,z)) has the edges: 0 > 0 Qed