YES Problem 1: (VAR v_NonEmpty:S x1:S) (RULES 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ) Problem 1: Dependency Pairs Processor: -> Pairs: 0#(0(1(0(x1:S)))) -> 0#(0(2(0(x1:S)))) 0#(0(1(0(x1:S)))) -> 0#(1(5(0(0(2(x1:S)))))) 0#(0(1(0(x1:S)))) -> 0#(2(0(x1:S))) 0#(3(1(0(x1:S)))) -> 0#(5(0(x1:S))) 0#(3(1(0(x1:S)))) -> 3#(0(5(0(x1:S)))) 0#(3(1(0(x1:S)))) -> 5#(0(x1:S)) 0#(1(0(0(0(x1:S))))) -> 0#(0(5(1(0(0(x1:S)))))) 0#(1(0(0(0(x1:S))))) -> 0#(5(1(0(0(x1:S))))) 0#(1(0(0(0(x1:S))))) -> 5#(1(0(0(x1:S)))) 0#(1(0(3(x1:S)))) -> 0#(5(3(2(0(x1:S))))) 0#(1(0(3(x1:S)))) -> 0#(x1:S) 0#(1(0(3(x1:S)))) -> 3#(2(0(x1:S))) 0#(1(0(3(x1:S)))) -> 5#(3(2(0(x1:S)))) 0#(1(0(x1:S))) -> 0#(0(2(0(x1:S)))) 0#(1(0(x1:S))) -> 0#(0(2(1(0(x1:S))))) 0#(1(0(x1:S))) -> 0#(3(2(1(0(x1:S))))) 0#(1(0(x1:S))) -> 0#(5(2(5(1(0(x1:S)))))) 0#(1(0(x1:S))) -> 0#(5(2(1(2(0(x1:S)))))) 0#(1(0(x1:S))) -> 0#(2(0(x1:S))) 0#(1(0(x1:S))) -> 0#(2(1(0(x1:S)))) 0#(1(0(x1:S))) -> 0#(4(0(4(1(3(x1:S)))))) 0#(1(0(x1:S))) -> 0#(4(0(x1:S))) 0#(1(0(x1:S))) -> 0#(4(1(3(x1:S)))) 0#(1(0(x1:S))) -> 0#(4(2(0(x1:S)))) 0#(1(0(x1:S))) -> 0#(4(2(2(1(0(x1:S)))))) 0#(1(0(x1:S))) -> 0#(4(4(4(0(x1:S))))) 0#(1(0(x1:S))) -> 3#(2(1(0(x1:S)))) 0#(1(0(x1:S))) -> 3#(x1:S) 0#(1(0(x1:S))) -> 5#(1(0(2(0(x1:S))))) 0#(1(0(x1:S))) -> 5#(1(0(4(0(x1:S))))) 0#(1(0(x1:S))) -> 5#(1(0(x1:S))) 0#(1(0(x1:S))) -> 5#(2(5(1(0(x1:S))))) 0#(1(0(x1:S))) -> 5#(2(1(2(0(x1:S))))) 0#(1(5(0(x1:S)))) -> 0#(5(1(4(0(x1:S))))) 0#(1(5(0(x1:S)))) -> 0#(2(0(x1:S))) 0#(1(5(0(x1:S)))) -> 3#(0(2(0(x1:S)))) 0#(1(5(0(x1:S)))) -> 5#(3(0(2(0(x1:S))))) 0#(1(5(0(x1:S)))) -> 5#(1(4(0(x1:S)))) 0#(1(1(0(x1:S)))) -> 0#(4(4(1(1(0(x1:S)))))) 0#(1(1(3(x1:S)))) -> 0#(x1:S) 0#(1(1(3(x1:S)))) -> 3#(4(5(1(1(0(x1:S)))))) 0#(1(1(3(x1:S)))) -> 5#(1(1(0(x1:S)))) 0#(1(2(0(x1:S)))) -> 0#(2(0(x1:S))) 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 0#(1(2(0(x1:S)))) -> 0#(4(0(x1:S))) 0#(1(2(0(x1:S)))) -> 3#(0(2(1(0(x1:S))))) 0#(1(4(0(0(x1:S))))) -> 0#(0(0(4(1(0(x1:S)))))) 0#(1(4(0(0(x1:S))))) -> 0#(0(4(1(0(x1:S))))) 0#(1(4(0(0(x1:S))))) -> 0#(4(1(0(x1:S)))) 0#(1(4(0(x1:S)))) -> 0#(3(4(2(1(0(x1:S)))))) 0#(1(4(0(x1:S)))) -> 3#(4(2(1(0(x1:S))))) 3#(0(3(1(0(x1:S))))) -> 0#(1(3(2(3(0(x1:S)))))) 3#(0(3(1(0(x1:S))))) -> 3#(0(x1:S)) 3#(0(3(1(0(x1:S))))) -> 3#(2(3(0(x1:S)))) 5#(0(1(0(x1:S)))) -> 0#(0(4(5(x1:S)))) 5#(0(1(0(x1:S)))) -> 0#(4(5(x1:S))) 5#(0(1(0(x1:S)))) -> 5#(x1:S) 5#(0(1(2(0(x1:S))))) -> 0#(0(5(2(1(0(x1:S)))))) 5#(0(1(2(0(x1:S))))) -> 0#(5(2(1(0(x1:S))))) 5#(0(1(2(0(x1:S))))) -> 5#(2(1(0(x1:S)))) -> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) Problem 1: SCC Processor: -> Pairs: 0#(0(1(0(x1:S)))) -> 0#(0(2(0(x1:S)))) 0#(0(1(0(x1:S)))) -> 0#(1(5(0(0(2(x1:S)))))) 0#(0(1(0(x1:S)))) -> 0#(2(0(x1:S))) 0#(3(1(0(x1:S)))) -> 0#(5(0(x1:S))) 0#(3(1(0(x1:S)))) -> 3#(0(5(0(x1:S)))) 0#(3(1(0(x1:S)))) -> 5#(0(x1:S)) 0#(1(0(0(0(x1:S))))) -> 0#(0(5(1(0(0(x1:S)))))) 0#(1(0(0(0(x1:S))))) -> 0#(5(1(0(0(x1:S))))) 0#(1(0(0(0(x1:S))))) -> 5#(1(0(0(x1:S)))) 0#(1(0(3(x1:S)))) -> 0#(5(3(2(0(x1:S))))) 0#(1(0(3(x1:S)))) -> 0#(x1:S) 0#(1(0(3(x1:S)))) -> 3#(2(0(x1:S))) 0#(1(0(3(x1:S)))) -> 5#(3(2(0(x1:S)))) 0#(1(0(x1:S))) -> 0#(0(2(0(x1:S)))) 0#(1(0(x1:S))) -> 0#(0(2(1(0(x1:S))))) 0#(1(0(x1:S))) -> 0#(3(2(1(0(x1:S))))) 0#(1(0(x1:S))) -> 0#(5(2(5(1(0(x1:S)))))) 0#(1(0(x1:S))) -> 0#(5(2(1(2(0(x1:S)))))) 0#(1(0(x1:S))) -> 0#(2(0(x1:S))) 0#(1(0(x1:S))) -> 0#(2(1(0(x1:S)))) 0#(1(0(x1:S))) -> 0#(4(0(4(1(3(x1:S)))))) 0#(1(0(x1:S))) -> 0#(4(0(x1:S))) 0#(1(0(x1:S))) -> 0#(4(1(3(x1:S)))) 0#(1(0(x1:S))) -> 0#(4(2(0(x1:S)))) 0#(1(0(x1:S))) -> 0#(4(2(2(1(0(x1:S)))))) 0#(1(0(x1:S))) -> 0#(4(4(4(0(x1:S))))) 0#(1(0(x1:S))) -> 3#(2(1(0(x1:S)))) 0#(1(0(x1:S))) -> 3#(x1:S) 0#(1(0(x1:S))) -> 5#(1(0(2(0(x1:S))))) 0#(1(0(x1:S))) -> 5#(1(0(4(0(x1:S))))) 0#(1(0(x1:S))) -> 5#(1(0(x1:S))) 0#(1(0(x1:S))) -> 5#(2(5(1(0(x1:S))))) 0#(1(0(x1:S))) -> 5#(2(1(2(0(x1:S))))) 0#(1(5(0(x1:S)))) -> 0#(5(1(4(0(x1:S))))) 0#(1(5(0(x1:S)))) -> 0#(2(0(x1:S))) 0#(1(5(0(x1:S)))) -> 3#(0(2(0(x1:S)))) 0#(1(5(0(x1:S)))) -> 5#(3(0(2(0(x1:S))))) 0#(1(5(0(x1:S)))) -> 5#(1(4(0(x1:S)))) 0#(1(1(0(x1:S)))) -> 0#(4(4(1(1(0(x1:S)))))) 0#(1(1(3(x1:S)))) -> 0#(x1:S) 0#(1(1(3(x1:S)))) -> 3#(4(5(1(1(0(x1:S)))))) 0#(1(1(3(x1:S)))) -> 5#(1(1(0(x1:S)))) 0#(1(2(0(x1:S)))) -> 0#(2(0(x1:S))) 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 0#(1(2(0(x1:S)))) -> 0#(4(0(x1:S))) 0#(1(2(0(x1:S)))) -> 3#(0(2(1(0(x1:S))))) 0#(1(4(0(0(x1:S))))) -> 0#(0(0(4(1(0(x1:S)))))) 0#(1(4(0(0(x1:S))))) -> 0#(0(4(1(0(x1:S))))) 0#(1(4(0(0(x1:S))))) -> 0#(4(1(0(x1:S)))) 0#(1(4(0(x1:S)))) -> 0#(3(4(2(1(0(x1:S)))))) 0#(1(4(0(x1:S)))) -> 3#(4(2(1(0(x1:S))))) 3#(0(3(1(0(x1:S))))) -> 0#(1(3(2(3(0(x1:S)))))) 3#(0(3(1(0(x1:S))))) -> 3#(0(x1:S)) 3#(0(3(1(0(x1:S))))) -> 3#(2(3(0(x1:S)))) 5#(0(1(0(x1:S)))) -> 0#(0(4(5(x1:S)))) 5#(0(1(0(x1:S)))) -> 0#(4(5(x1:S))) 5#(0(1(0(x1:S)))) -> 5#(x1:S) 5#(0(1(2(0(x1:S))))) -> 0#(0(5(2(1(0(x1:S)))))) 5#(0(1(2(0(x1:S))))) -> 0#(5(2(1(0(x1:S))))) 5#(0(1(2(0(x1:S))))) -> 5#(2(1(0(x1:S)))) -> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(0(1(0(x1:S)))) -> 5#(x1:S) ->->-> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->->Cycle: ->->-> Pairs: 3#(0(3(1(0(x1:S))))) -> 3#(0(x1:S)) ->->-> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->->Cycle: ->->-> Pairs: 0#(3(1(0(x1:S)))) -> 0#(5(0(x1:S))) 0#(1(0(3(x1:S)))) -> 0#(x1:S) 0#(1(1(3(x1:S)))) -> 0#(x1:S) ->->-> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) The problem is decomposed in 3 subproblems. Problem 1.1: Subterm Processor: -> Pairs: 5#(0(1(0(x1:S)))) -> 5#(x1:S) -> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->Projection: pi(5#) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: 3#(0(3(1(0(x1:S))))) -> 3#(0(x1:S)) -> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->Projection: pi(3#) = 1 Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.3: Reduction Pair Processor: -> Pairs: 0#(3(1(0(x1:S)))) -> 0#(5(0(x1:S))) 0#(1(0(3(x1:S)))) -> 0#(x1:S) 0#(1(1(3(x1:S)))) -> 0#(x1:S) -> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) -> Usable rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X [3](X) = 2.X + 1/2 [5](X) = 1/2.X [1](X) = X + 2 [2](X) = 0 [4](X) = 0 [0#](X) = 2.X Problem 1.3: SCC Processor: -> Pairs: 0#(1(0(3(x1:S)))) -> 0#(x1:S) 0#(1(1(3(x1:S)))) -> 0#(x1:S) -> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(0(3(x1:S)))) -> 0#(x1:S) 0#(1(1(3(x1:S)))) -> 0#(x1:S) ->->-> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) Problem 1.3: Subterm Processor: -> Pairs: 0#(1(0(3(x1:S)))) -> 0#(x1:S) 0#(1(1(3(x1:S)))) -> 0#(x1:S) -> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->Projection: pi(0#) = 1 Problem 1.3: SCC Processor: -> Pairs: Empty -> Rules: 0(0(1(0(x1:S)))) -> 0(1(5(0(0(2(x1:S)))))) 0(0(1(0(x1:S)))) -> 1(0(0(2(0(x1:S))))) 0(3(0(1(0(x1:S))))) -> 0(3(0(0(2(1(x1:S)))))) 0(3(1(0(x1:S)))) -> 1(2(3(0(5(0(x1:S)))))) 0(1(0(0(0(x1:S))))) -> 0(0(5(1(0(0(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(3(3(0(2(x1:S)))))) 0(1(0(3(x1:S)))) -> 1(0(5(3(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(0(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(0(2(1(2(x1:S))))) 0(1(0(x1:S))) -> 0(3(2(1(0(x1:S))))) 0(1(0(x1:S))) -> 0(5(2(5(1(0(x1:S)))))) 0(1(0(x1:S))) -> 0(5(2(1(2(0(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(3(2(x1:S)))))) 0(1(0(x1:S))) -> 0(2(1(0(2(x1:S))))) 0(1(0(x1:S))) -> 0(2(1(0(x1:S)))) 0(1(0(x1:S))) -> 0(4(0(4(1(3(x1:S)))))) 0(1(0(x1:S))) -> 0(4(2(2(1(0(x1:S)))))) 0(1(0(x1:S))) -> 3(0(0(4(1(4(x1:S)))))) 0(1(0(x1:S))) -> 5(0(0(4(1(x1:S))))) 0(1(0(x1:S))) -> 5(5(1(0(0(2(x1:S)))))) 0(1(0(x1:S))) -> 5(1(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(0(2(x1:S))))) 0(1(0(x1:S))) -> 1(0(0(5(4(4(x1:S)))))) 0(1(0(x1:S))) -> 1(0(0(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(2(0(x1:S))))) 0(1(0(x1:S))) -> 1(0(4(4(4(0(x1:S)))))) 0(1(0(x1:S))) -> 1(5(0(0(4(2(x1:S)))))) 0(1(0(x1:S))) -> 1(4(0(4(0(x1:S))))) 0(1(0(x1:S))) -> 4(0(0(2(1(x1:S))))) 0(1(0(x1:S))) -> 4(5(1(0(2(0(x1:S)))))) 0(1(3(0(x1:S)))) -> 1(0(3(0(2(x1:S))))) 0(1(5(0(x1:S)))) -> 0(5(1(4(0(x1:S))))) 0(1(5(0(x1:S)))) -> 1(5(3(0(2(0(x1:S)))))) 0(1(1(0(x1:S)))) -> 0(4(4(1(1(0(x1:S)))))) 0(1(1(3(x1:S)))) -> 3(4(5(1(1(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 0(0(4(2(5(1(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(4(x1:S)))))) 0(1(2(0(x1:S)))) -> 3(0(2(1(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(0(2(0(x1:S))))) 0(1(2(0(x1:S)))) -> 1(1(2(0(4(0(x1:S)))))) 0(1(2(0(x1:S)))) -> 4(1(0(0(2(x1:S))))) 0(1(2(5(0(x1:S))))) -> 1(0(2(0(5(4(x1:S)))))) 0(1(2(4(0(x1:S))))) -> 0(0(5(4(2(1(x1:S)))))) 0(1(4(0(0(x1:S))))) -> 0(0(0(4(1(0(x1:S)))))) 0(1(4(0(x1:S)))) -> 0(3(4(2(1(0(x1:S)))))) 0(1(4(5(0(x1:S))))) -> 1(5(0(0(4(2(x1:S)))))) 3(0(3(1(0(x1:S))))) -> 0(1(3(2(3(0(x1:S)))))) 5(0(1(0(x1:S)))) -> 1(4(0(0(5(1(x1:S)))))) 5(0(1(0(x1:S)))) -> 2(1(0(0(4(5(x1:S)))))) 5(0(1(2(0(x1:S))))) -> 0(0(5(2(1(0(x1:S)))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite.