/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) 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) 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) 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) 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) graph: *#(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: 2 #rules: 7 #arcs: 52/144 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) 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) 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) 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) 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) 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) The DP: +#(O(x),O(y)) -> +#(x,y) has the edges: 0 > 0 1 > 1 Qed