/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: isLeaf(leaf()) -> true() isLeaf(cons(u,v)) -> false() left(cons(u,v)) -> u right(cons(u,v)) -> v concat(leaf(),y) -> y concat(cons(u,v),y) -> cons(u,concat(v,y)) less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v) if1(b,true(),u,v) -> false() if1(b,false(),u,v) -> if2(b,u,v) if2(true(),u,v) -> true() if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v))) Proof: DP Processor: DPs: concat#(cons(u,v),y) -> concat#(v,y) less_leaves#(u,v) -> isLeaf#(v) less_leaves#(u,v) -> isLeaf#(u) less_leaves#(u,v) -> if1#(isLeaf(u),isLeaf(v),u,v) if1#(b,false(),u,v) -> if2#(b,u,v) if2#(false(),u,v) -> right#(v) if2#(false(),u,v) -> left#(v) if2#(false(),u,v) -> concat#(left(v),right(v)) if2#(false(),u,v) -> right#(u) if2#(false(),u,v) -> left#(u) if2#(false(),u,v) -> concat#(left(u),right(u)) if2#(false(),u,v) -> less_leaves#(concat(left(u),right(u)),concat(left(v),right(v))) TRS: isLeaf(leaf()) -> true() isLeaf(cons(u,v)) -> false() left(cons(u,v)) -> u right(cons(u,v)) -> v concat(leaf(),y) -> y concat(cons(u,v),y) -> cons(u,concat(v,y)) less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v) if1(b,true(),u,v) -> false() if1(b,false(),u,v) -> if2(b,u,v) if2(true(),u,v) -> true() if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v))) TDG Processor: DPs: concat#(cons(u,v),y) -> concat#(v,y) less_leaves#(u,v) -> isLeaf#(v) less_leaves#(u,v) -> isLeaf#(u) less_leaves#(u,v) -> if1#(isLeaf(u),isLeaf(v),u,v) if1#(b,false(),u,v) -> if2#(b,u,v) if2#(false(),u,v) -> right#(v) if2#(false(),u,v) -> left#(v) if2#(false(),u,v) -> concat#(left(v),right(v)) if2#(false(),u,v) -> right#(u) if2#(false(),u,v) -> left#(u) if2#(false(),u,v) -> concat#(left(u),right(u)) if2#(false(),u,v) -> less_leaves#(concat(left(u),right(u)),concat(left(v),right(v))) TRS: isLeaf(leaf()) -> true() isLeaf(cons(u,v)) -> false() left(cons(u,v)) -> u right(cons(u,v)) -> v concat(leaf(),y) -> y concat(cons(u,v),y) -> cons(u,concat(v,y)) less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v) if1(b,true(),u,v) -> false() if1(b,false(),u,v) -> if2(b,u,v) if2(true(),u,v) -> true() if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v))) graph: if2#(false(),u,v) -> less_leaves#(concat(left(u),right(u)),concat(left(v),right(v))) -> less_leaves#(u,v) -> if1#(isLeaf(u),isLeaf(v),u,v) if2#(false(),u,v) -> less_leaves#(concat(left(u),right(u)),concat(left(v),right(v))) -> less_leaves#(u,v) -> isLeaf#(u) if2#(false(),u,v) -> less_leaves#(concat(left(u),right(u)),concat(left(v),right(v))) -> less_leaves#(u,v) -> isLeaf#(v) if2#(false(),u,v) -> concat#(left(v),right(v)) -> concat#(cons(u,v),y) -> concat#(v,y) if2#(false(),u,v) -> concat#(left(u),right(u)) -> concat#(cons(u,v),y) -> concat#(v,y) if1#(b,false(),u,v) -> if2#(b,u,v) -> if2#(false(),u,v) -> less_leaves#(concat(left(u),right(u)),concat(left(v),right(v))) if1#(b,false(),u,v) -> if2#(b,u,v) -> if2#(false(),u,v) -> concat#(left(u),right(u)) if1#(b,false(),u,v) -> if2#(b,u,v) -> if2#(false(),u,v) -> left#(u) if1#(b,false(),u,v) -> if2#(b,u,v) -> if2#(false(),u,v) -> right#(u) if1#(b,false(),u,v) -> if2#(b,u,v) -> if2#(false(),u,v) -> concat#(left(v),right(v)) if1#(b,false(),u,v) -> if2#(b,u,v) -> if2#(false(),u,v) -> left#(v) if1#(b,false(),u,v) -> if2#(b,u,v) -> if2#(false(),u,v) -> right#(v) less_leaves#(u,v) -> if1#(isLeaf(u),isLeaf(v),u,v) -> if1#(b,false(),u,v) -> if2#(b,u,v) concat#(cons(u,v),y) -> concat#(v,y) -> concat#(cons(u,v),y) -> concat#(v,y) SCC Processor: #sccs: 2 #rules: 4 #arcs: 14/144 DPs: if2#(false(),u,v) -> less_leaves#(concat(left(u),right(u)),concat(left(v),right(v))) less_leaves#(u,v) -> if1#(isLeaf(u),isLeaf(v),u,v) if1#(b,false(),u,v) -> if2#(b,u,v) TRS: isLeaf(leaf()) -> true() isLeaf(cons(u,v)) -> false() left(cons(u,v)) -> u right(cons(u,v)) -> v concat(leaf(),y) -> y concat(cons(u,v),y) -> cons(u,concat(v,y)) less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v) if1(b,true(),u,v) -> false() if1(b,false(),u,v) -> if2(b,u,v) if2(true(),u,v) -> true() if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v))) EDG Processor: DPs: if2#(false(),u,v) -> less_leaves#(concat(left(u),right(u)),concat(left(v),right(v))) less_leaves#(u,v) -> if1#(isLeaf(u),isLeaf(v),u,v) if1#(b,false(),u,v) -> if2#(b,u,v) TRS: isLeaf(leaf()) -> true() isLeaf(cons(u,v)) -> false() left(cons(u,v)) -> u right(cons(u,v)) -> v concat(leaf(),y) -> y concat(cons(u,v),y) -> cons(u,concat(v,y)) less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v) if1(b,true(),u,v) -> false() if1(b,false(),u,v) -> if2(b,u,v) if2(true(),u,v) -> true() if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v))) graph: if1#(b,false(),u,v) -> if2#(b,u,v) -> if2#(false(),u,v) -> less_leaves#(concat(left(u),right(u)),concat(left(v),right(v))) less_leaves#(u,v) -> if1#(isLeaf(u),isLeaf(v),u,v) -> if1#(b,false(),u,v) -> if2#(b,u,v) SCC Processor: #sccs: 0 #rules: 0 #arcs: 2/9 DPs: concat#(cons(u,v),y) -> concat#(v,y) TRS: isLeaf(leaf()) -> true() isLeaf(cons(u,v)) -> false() left(cons(u,v)) -> u right(cons(u,v)) -> v concat(leaf(),y) -> y concat(cons(u,v),y) -> cons(u,concat(v,y)) less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v) if1(b,true(),u,v) -> false() if1(b,false(),u,v) -> if2(b,u,v) if2(true(),u,v) -> true() if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v))) Subterm Criterion Processor: simple projection: pi(concat#) = 0 problem: DPs: TRS: isLeaf(leaf()) -> true() isLeaf(cons(u,v)) -> false() left(cons(u,v)) -> u right(cons(u,v)) -> v concat(leaf(),y) -> y concat(cons(u,v),y) -> cons(u,concat(v,y)) less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v) if1(b,true(),u,v) -> false() if1(b,false(),u,v) -> if2(b,u,v) if2(true(),u,v) -> true() if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v))) Qed