/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: ack(0(),y) -> s(y) ack(s(x),0()) -> ack(x,s(0())) ack(s(x),s(y)) -> ack(x,ack(s(x),y)) f(s(x),y) -> f(x,s(x)) f(x,s(y)) -> f(y,x) f(x,y) -> ack(x,y) ack(s(x),y) -> f(x,x) Proof: DP Processor: DPs: ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) f#(s(x),y) -> f#(x,s(x)) f#(x,s(y)) -> f#(y,x) f#(x,y) -> ack#(x,y) ack#(s(x),y) -> f#(x,x) TRS: ack(0(),y) -> s(y) ack(s(x),0()) -> ack(x,s(0())) ack(s(x),s(y)) -> ack(x,ack(s(x),y)) f(s(x),y) -> f(x,s(x)) f(x,s(y)) -> f(y,x) f(x,y) -> ack(x,y) ack(s(x),y) -> f(x,x) TDG Processor: DPs: ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) f#(s(x),y) -> f#(x,s(x)) f#(x,s(y)) -> f#(y,x) f#(x,y) -> ack#(x,y) ack#(s(x),y) -> f#(x,x) TRS: ack(0(),y) -> s(y) ack(s(x),0()) -> ack(x,s(0())) ack(s(x),s(y)) -> ack(x,ack(s(x),y)) f(s(x),y) -> f(x,s(x)) f(x,s(y)) -> f(y,x) f(x,y) -> ack(x,y) ack(s(x),y) -> f(x,x) graph: f#(s(x),y) -> f#(x,s(x)) -> f#(x,y) -> ack#(x,y) f#(s(x),y) -> f#(x,s(x)) -> f#(x,s(y)) -> f#(y,x) f#(s(x),y) -> f#(x,s(x)) -> f#(s(x),y) -> f#(x,s(x)) f#(x,s(y)) -> f#(y,x) -> f#(x,y) -> ack#(x,y) f#(x,s(y)) -> f#(y,x) -> f#(x,s(y)) -> f#(y,x) f#(x,s(y)) -> f#(y,x) -> f#(s(x),y) -> f#(x,s(x)) f#(x,y) -> ack#(x,y) -> ack#(s(x),y) -> f#(x,x) f#(x,y) -> ack#(x,y) -> ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) f#(x,y) -> ack#(x,y) -> ack#(s(x),s(y)) -> ack#(s(x),y) f#(x,y) -> ack#(x,y) -> ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),y) -> f#(x,x) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) -> ack#(s(x),y) -> f#(x,x) ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) -> ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) -> ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) -> ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),y) -> f#(x,x) ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),y) -> f#(x,x) -> f#(x,y) -> ack#(x,y) ack#(s(x),y) -> f#(x,x) -> f#(x,s(y)) -> f#(y,x) ack#(s(x),y) -> f#(x,x) -> f#(s(x),y) -> f#(x,s(x)) EDG Processor: DPs: ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) f#(s(x),y) -> f#(x,s(x)) f#(x,s(y)) -> f#(y,x) f#(x,y) -> ack#(x,y) ack#(s(x),y) -> f#(x,x) TRS: ack(0(),y) -> s(y) ack(s(x),0()) -> ack(x,s(0())) ack(s(x),s(y)) -> ack(x,ack(s(x),y)) f(s(x),y) -> f(x,s(x)) f(x,s(y)) -> f(y,x) f(x,y) -> ack(x,y) ack(s(x),y) -> f(x,x) graph: f#(s(x),y) -> f#(x,s(x)) -> f#(s(x),y) -> f#(x,s(x)) f#(s(x),y) -> f#(x,s(x)) -> f#(x,s(y)) -> f#(y,x) f#(s(x),y) -> f#(x,s(x)) -> f#(x,y) -> ack#(x,y) f#(x,s(y)) -> f#(y,x) -> f#(s(x),y) -> f#(x,s(x)) f#(x,s(y)) -> f#(y,x) -> f#(x,s(y)) -> f#(y,x) f#(x,s(y)) -> f#(y,x) -> f#(x,y) -> ack#(x,y) f#(x,y) -> ack#(x,y) -> ack#(s(x),0()) -> ack#(x,s(0())) f#(x,y) -> ack#(x,y) -> ack#(s(x),s(y)) -> ack#(s(x),y) f#(x,y) -> ack#(x,y) -> ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) f#(x,y) -> ack#(x,y) -> ack#(s(x),y) -> f#(x,x) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),y) -> f#(x,x) ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) -> ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) -> ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) -> ack#(s(x),y) -> f#(x,x) ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),y) -> f#(x,x) ack#(s(x),y) -> f#(x,x) -> f#(s(x),y) -> f#(x,s(x)) ack#(s(x),y) -> f#(x,x) -> f#(x,s(y)) -> f#(y,x) ack#(s(x),y) -> f#(x,x) -> f#(x,y) -> ack#(x,y) Size-Change Termination Processor: DPs: TRS: ack(0(),y) -> s(y) ack(s(x),0()) -> ack(x,s(0())) ack(s(x),s(y)) -> ack(x,ack(s(x),y)) f(s(x),y) -> f(x,s(x)) f(x,s(y)) -> f(y,x) f(x,y) -> ack(x,y) ack(s(x),y) -> f(x,x) The DP: ack#(s(x),0()) -> ack#(x,s(0())) has the edges: 0 > 0 The DP: ack#(s(x),s(y)) -> ack#(s(x),y) has the edges: 0 >= 0 1 > 1 The DP: ack#(s(x),s(y)) -> ack#(x,ack(s(x),y)) has the edges: 0 > 0 The DP: f#(s(x),y) -> f#(x,s(x)) has the edges: 0 >= 1 0 > 0 The DP: f#(x,s(y)) -> f#(y,x) has the edges: 0 >= 1 1 > 0 The DP: f#(x,y) -> ack#(x,y) has the edges: 0 >= 0 1 >= 1 The DP: ack#(s(x),y) -> f#(x,x) has the edges: 0 > 1 0 > 0 Qed