/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: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) Proof: DP Processor: DPs: +#(O(x),O(y)) -> +#(x,y) +#(O(x),O(y)) -> O#(+(x,y)) +#(O(x),I(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(I(x),I(y)) -> O#(+(+(x,y),I(0()))) *#(O(x),y) -> *#(x,y) *#(O(x),y) -> O#(*(x,y)) *#(I(x),y) -> *#(x,y) *#(I(x),y) -> O#(*(x,y)) *#(I(x),y) -> +#(O(*(x,y)),y) -#(O(x),O(y)) -> -#(x,y) -#(O(x),O(y)) -> O#(-(x,y)) -#(O(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(I(x),O(y)) -> -#(x,y) -#(I(x),I(y)) -> -#(x,y) -#(I(x),I(y)) -> O#(-(x,y)) TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) TDG Processor: DPs: +#(O(x),O(y)) -> +#(x,y) +#(O(x),O(y)) -> O#(+(x,y)) +#(O(x),I(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(I(x),I(y)) -> O#(+(+(x,y),I(0()))) *#(O(x),y) -> *#(x,y) *#(O(x),y) -> O#(*(x,y)) *#(I(x),y) -> *#(x,y) *#(I(x),y) -> O#(*(x,y)) *#(I(x),y) -> +#(O(*(x,y)),y) -#(O(x),O(y)) -> -#(x,y) -#(O(x),O(y)) -> O#(-(x,y)) -#(O(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(I(x),O(y)) -> -#(x,y) -#(I(x),I(y)) -> -#(x,y) -#(I(x),I(y)) -> O#(-(x,y)) TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) graph: -#(I(x),I(y)) -> -#(x,y) -> -#(I(x),I(y)) -> O#(-(x,y)) -#(I(x),I(y)) -> -#(x,y) -> -#(I(x),I(y)) -> -#(x,y) -#(I(x),I(y)) -> -#(x,y) -> -#(I(x),O(y)) -> -#(x,y) -#(I(x),I(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(I(x),I(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(x,y) -#(I(x),I(y)) -> -#(x,y) -> -#(O(x),O(y)) -> O#(-(x,y)) -#(I(x),I(y)) -> -#(x,y) -> -#(O(x),O(y)) -> -#(x,y) -#(I(x),O(y)) -> -#(x,y) -> -#(I(x),I(y)) -> O#(-(x,y)) -#(I(x),O(y)) -> -#(x,y) -> -#(I(x),I(y)) -> -#(x,y) -#(I(x),O(y)) -> -#(x,y) -> -#(I(x),O(y)) -> -#(x,y) -#(I(x),O(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(I(x),O(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(x,y) -#(I(x),O(y)) -> -#(x,y) -> -#(O(x),O(y)) -> O#(-(x,y)) -#(I(x),O(y)) -> -#(x,y) -> -#(O(x),O(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -> -#(I(x),I(y)) -> O#(-(x,y)) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -> -#(I(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -> -#(I(x),O(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -> -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -> -#(O(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -> -#(O(x),O(y)) -> O#(-(x,y)) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -> -#(O(x),O(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(x,y) -> -#(I(x),I(y)) -> O#(-(x,y)) -#(O(x),I(y)) -> -#(x,y) -> -#(I(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(x,y) -> -#(I(x),O(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(O(x),I(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(x,y) -> -#(O(x),O(y)) -> O#(-(x,y)) -#(O(x),I(y)) -> -#(x,y) -> -#(O(x),O(y)) -> -#(x,y) -#(O(x),O(y)) -> -#(x,y) -> -#(I(x),I(y)) -> O#(-(x,y)) -#(O(x),O(y)) -> -#(x,y) -> -#(I(x),I(y)) -> -#(x,y) -#(O(x),O(y)) -> -#(x,y) -> -#(I(x),O(y)) -> -#(x,y) -#(O(x),O(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(O(x),O(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(x,y) -#(O(x),O(y)) -> -#(x,y) -> -#(O(x),O(y)) -> O#(-(x,y)) -#(O(x),O(y)) -> -#(x,y) -> -#(O(x),O(y)) -> -#(x,y) *#(I(x),y) -> *#(x,y) -> *#(I(x),y) -> +#(O(*(x,y)),y) *#(I(x),y) -> *#(x,y) -> *#(I(x),y) -> O#(*(x,y)) *#(I(x),y) -> *#(x,y) -> *#(I(x),y) -> *#(x,y) *#(I(x),y) -> *#(x,y) -> *#(O(x),y) -> O#(*(x,y)) *#(I(x),y) -> *#(x,y) -> *#(O(x),y) -> *#(x,y) *#(I(x),y) -> +#(O(*(x,y)),y) -> +#(I(x),I(y)) -> O#(+(+(x,y),I(0()))) *#(I(x),y) -> +#(O(*(x,y)),y) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) *#(I(x),y) -> +#(O(*(x,y)),y) -> +#(I(x),I(y)) -> +#(x,y) *#(I(x),y) -> +#(O(*(x,y)),y) -> +#(I(x),O(y)) -> +#(x,y) *#(I(x),y) -> +#(O(*(x,y)),y) -> +#(O(x),I(y)) -> +#(x,y) *#(I(x),y) -> +#(O(*(x,y)),y) -> +#(O(x),O(y)) -> O#(+(x,y)) *#(I(x),y) -> +#(O(*(x,y)),y) -> +#(O(x),O(y)) -> +#(x,y) *#(O(x),y) -> *#(x,y) -> *#(I(x),y) -> +#(O(*(x,y)),y) *#(O(x),y) -> *#(x,y) -> *#(I(x),y) -> O#(*(x,y)) *#(O(x),y) -> *#(x,y) -> *#(I(x),y) -> *#(x,y) *#(O(x),y) -> *#(x,y) -> *#(O(x),y) -> O#(*(x,y)) *#(O(x),y) -> *#(x,y) -> *#(O(x),y) -> *#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) -> +#(I(x),I(y)) -> O#(+(+(x,y),I(0()))) +#(I(x),I(y)) -> +#(+(x,y),I(0())) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(I(x),I(y)) -> +#(+(x,y),I(0())) -> +#(I(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) -> +#(I(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) -> +#(O(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) -> +#(O(x),O(y)) -> O#(+(x,y)) +#(I(x),I(y)) -> +#(+(x,y),I(0())) -> +#(O(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) -> +#(I(x),I(y)) -> O#(+(+(x,y),I(0()))) +#(I(x),I(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(I(x),I(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) -> +#(I(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) -> +#(O(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) -> +#(O(x),O(y)) -> O#(+(x,y)) +#(I(x),I(y)) -> +#(x,y) -> +#(O(x),O(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) -> +#(I(x),I(y)) -> O#(+(+(x,y),I(0()))) +#(I(x),O(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(I(x),O(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) -> +#(I(x),O(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) -> +#(O(x),I(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) -> +#(O(x),O(y)) -> O#(+(x,y)) +#(I(x),O(y)) -> +#(x,y) -> +#(O(x),O(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) -> +#(I(x),I(y)) -> O#(+(+(x,y),I(0()))) +#(O(x),I(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(O(x),I(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) -> +#(I(x),O(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) -> +#(O(x),I(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) -> +#(O(x),O(y)) -> O#(+(x,y)) +#(O(x),I(y)) -> +#(x,y) -> +#(O(x),O(y)) -> +#(x,y) +#(O(x),O(y)) -> +#(x,y) -> +#(I(x),I(y)) -> O#(+(+(x,y),I(0()))) +#(O(x),O(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(O(x),O(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(x,y) +#(O(x),O(y)) -> +#(x,y) -> +#(I(x),O(y)) -> +#(x,y) +#(O(x),O(y)) -> +#(x,y) -> +#(O(x),I(y)) -> +#(x,y) +#(O(x),O(y)) -> +#(x,y) -> +#(O(x),O(y)) -> O#(+(x,y)) +#(O(x),O(y)) -> +#(x,y) -> +#(O(x),O(y)) -> +#(x,y) SCC Processor: #sccs: 3 #rules: 12 #arcs: 87/361 DPs: *#(I(x),y) -> *#(x,y) *#(O(x),y) -> *#(x,y) TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) Subterm Criterion Processor: simple projection: pi(*#) = 0 problem: DPs: TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) Qed DPs: +#(O(x),O(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) EDG Processor: DPs: +#(O(x),O(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) graph: +#(I(x),I(y)) -> +#(+(x,y),I(0())) -> +#(O(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) -> +#(I(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(I(x),I(y)) -> +#(x,y) -> +#(O(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) -> +#(O(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) -> +#(I(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(I(x),O(y)) -> +#(x,y) -> +#(O(x),O(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) -> +#(O(x),I(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) -> +#(I(x),O(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(O(x),I(y)) -> +#(x,y) -> +#(O(x),O(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) -> +#(O(x),I(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) -> +#(I(x),O(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(O(x),O(y)) -> +#(x,y) -> +#(O(x),O(y)) -> +#(x,y) +#(O(x),O(y)) -> +#(x,y) -> +#(O(x),I(y)) -> +#(x,y) +#(O(x),O(y)) -> +#(x,y) -> +#(I(x),O(y)) -> +#(x,y) +#(O(x),O(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(x,y) +#(O(x),O(y)) -> +#(x,y) -> +#(I(x),I(y)) -> +#(+(x,y),I(0())) Usable Rule Processor: DPs: +#(O(x),O(y)) -> +#(x,y) +#(O(x),I(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) TRS: +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) O(0()) -> 0() Semantic Labeling Processor: dimension: 1 usable rules: interpretation: [I](x0) = x0 + 1, [+](x0, x1) = x0 + x1, [O](x0) = x0, [0] = 0 labeled: +# I + usable (for model): +# O I + 0 argument filtering: pi(0) = [] pi(O) = 0 pi(+) = 0 pi(I) = [] pi(+#) = [] precedence: +# ~ I ~ + ~ O ~ 0 problem: DPs: +#(O(x),O(y)) -> +#(x,y) TRS: +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) O(0()) -> 0() Restore Modifier: DPs: +#(O(x),O(y)) -> +#(x,y) TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) Size-Change Termination Processor: DPs: TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) The DP: +#(O(x),O(y)) -> +#(x,y) has the edges: 0 > 0 1 > 1 Qed DPs: -#(I(x),I(y)) -> -#(x,y) -#(O(x),O(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(I(x),O(y)) -> -#(x,y) TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) EDG Processor: DPs: -#(I(x),I(y)) -> -#(x,y) -#(O(x),O(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(I(x),O(y)) -> -#(x,y) TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) graph: -#(I(x),I(y)) -> -#(x,y) -> -#(O(x),O(y)) -> -#(x,y) -#(I(x),I(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(x,y) -#(I(x),I(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(I(x),I(y)) -> -#(x,y) -> -#(I(x),O(y)) -> -#(x,y) -#(I(x),I(y)) -> -#(x,y) -> -#(I(x),I(y)) -> -#(x,y) -#(I(x),O(y)) -> -#(x,y) -> -#(O(x),O(y)) -> -#(x,y) -#(I(x),O(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(x,y) -#(I(x),O(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(I(x),O(y)) -> -#(x,y) -> -#(I(x),O(y)) -> -#(x,y) -#(I(x),O(y)) -> -#(x,y) -> -#(I(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -> -#(O(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -> -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -> -#(I(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(x,y) -> -#(O(x),O(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(O(x),I(y)) -> -#(x,y) -> -#(I(x),O(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(x,y) -> -#(I(x),I(y)) -> -#(x,y) -#(O(x),O(y)) -> -#(x,y) -> -#(O(x),O(y)) -> -#(x,y) -#(O(x),O(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(x,y) -#(O(x),O(y)) -> -#(x,y) -> -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(O(x),O(y)) -> -#(x,y) -> -#(I(x),O(y)) -> -#(x,y) -#(O(x),O(y)) -> -#(x,y) -> -#(I(x),I(y)) -> -#(x,y) Subterm Criterion Processor: simple projection: pi(O) = [0,0] pi(I) = [0,0] pi(-) = 0 pi(-#) = [0,0] problem: DPs: TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) Qed