0.00/0.09 YES 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 (VAR v_NonEmpty:S x1:S) 0.00/0.09 (RULES 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ) 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 Dependency Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 0#(ql(x1:S)) -> 0#(x1:S) 0.00/0.09 0#(qr(x1:S)) -> 0#(x1:S) 0.00/0.09 1#(ql(x1:S)) -> 1#(x1:S) 0.00/0.09 1#(qr(x1:S)) -> 1#(x1:S) 0.00/0.09 B(ql(0(x1:S))) -> 0#(b(r0(x1:S))) 0.00/0.09 B(ql(0(x1:S))) -> B(r0(x1:S)) 0.00/0.09 B(ql(0(x1:S))) -> R0(x1:S) 0.00/0.09 B(ql(1(x1:S))) -> 1#(b(r1(x1:S))) 0.00/0.09 B(ql(1(x1:S))) -> B(r1(x1:S)) 0.00/0.09 B(ql(1(x1:S))) -> R1(x1:S) 0.00/0.09 M(qr(x1:S)) -> M(x1:S) 0.00/0.09 R0(0(x1:S)) -> 0#(r0(x1:S)) 0.00/0.09 R0(0(x1:S)) -> R0(x1:S) 0.00/0.09 R0(1(x1:S)) -> 1#(r0(x1:S)) 0.00/0.09 R0(1(x1:S)) -> R0(x1:S) 0.00/0.09 R0(b(x1:S)) -> 0#(b(x1:S)) 0.00/0.09 R0(m(x1:S)) -> M(r0(x1:S)) 0.00/0.09 R0(m(x1:S)) -> R0(x1:S) 0.00/0.09 R1(0(x1:S)) -> 0#(r1(x1:S)) 0.00/0.09 R1(0(x1:S)) -> R1(x1:S) 0.00/0.09 R1(1(x1:S)) -> 1#(r1(x1:S)) 0.00/0.09 R1(1(x1:S)) -> R1(x1:S) 0.00/0.09 R1(b(x1:S)) -> 1#(b(x1:S)) 0.00/0.09 R1(m(x1:S)) -> M(r1(x1:S)) 0.00/0.09 R1(m(x1:S)) -> R1(x1:S) 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 0#(ql(x1:S)) -> 0#(x1:S) 0.00/0.09 0#(qr(x1:S)) -> 0#(x1:S) 0.00/0.09 1#(ql(x1:S)) -> 1#(x1:S) 0.00/0.09 1#(qr(x1:S)) -> 1#(x1:S) 0.00/0.09 B(ql(0(x1:S))) -> 0#(b(r0(x1:S))) 0.00/0.09 B(ql(0(x1:S))) -> B(r0(x1:S)) 0.00/0.09 B(ql(0(x1:S))) -> R0(x1:S) 0.00/0.09 B(ql(1(x1:S))) -> 1#(b(r1(x1:S))) 0.00/0.09 B(ql(1(x1:S))) -> B(r1(x1:S)) 0.00/0.09 B(ql(1(x1:S))) -> R1(x1:S) 0.00/0.09 M(qr(x1:S)) -> M(x1:S) 0.00/0.09 R0(0(x1:S)) -> 0#(r0(x1:S)) 0.00/0.09 R0(0(x1:S)) -> R0(x1:S) 0.00/0.09 R0(1(x1:S)) -> 1#(r0(x1:S)) 0.00/0.09 R0(1(x1:S)) -> R0(x1:S) 0.00/0.09 R0(b(x1:S)) -> 0#(b(x1:S)) 0.00/0.09 R0(m(x1:S)) -> M(r0(x1:S)) 0.00/0.09 R0(m(x1:S)) -> R0(x1:S) 0.00/0.09 R1(0(x1:S)) -> 0#(r1(x1:S)) 0.00/0.09 R1(0(x1:S)) -> R1(x1:S) 0.00/0.09 R1(1(x1:S)) -> 1#(r1(x1:S)) 0.00/0.09 R1(1(x1:S)) -> R1(x1:S) 0.00/0.09 R1(b(x1:S)) -> 1#(b(x1:S)) 0.00/0.09 R1(m(x1:S)) -> M(r1(x1:S)) 0.00/0.09 R1(m(x1:S)) -> R1(x1:S) 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 M(qr(x1:S)) -> M(x1:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 1#(ql(x1:S)) -> 1#(x1:S) 0.00/0.09 1#(qr(x1:S)) -> 1#(x1:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 0#(ql(x1:S)) -> 0#(x1:S) 0.00/0.09 0#(qr(x1:S)) -> 0#(x1:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 R0(0(x1:S)) -> R0(x1:S) 0.00/0.09 R0(1(x1:S)) -> R0(x1:S) 0.00/0.09 R0(m(x1:S)) -> R0(x1:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 R1(0(x1:S)) -> R1(x1:S) 0.00/0.09 R1(1(x1:S)) -> R1(x1:S) 0.00/0.09 R1(m(x1:S)) -> R1(x1:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 B(ql(0(x1:S))) -> B(r0(x1:S)) 0.00/0.09 B(ql(1(x1:S))) -> B(r1(x1:S)) 0.00/0.09 ->->-> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 0.00/0.09 0.00/0.09 The problem is decomposed in 6 subproblems. 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 M(qr(x1:S)) -> M(x1:S) 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Projection: 0.00/0.09 pi(M) = 1 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.2: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 1#(ql(x1:S)) -> 1#(x1:S) 0.00/0.09 1#(qr(x1:S)) -> 1#(x1:S) 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Projection: 0.00/0.09 pi(1#) = 1 0.00/0.09 0.00/0.09 Problem 1.2: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.3: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 0#(ql(x1:S)) -> 0#(x1:S) 0.00/0.09 0#(qr(x1:S)) -> 0#(x1:S) 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Projection: 0.00/0.09 pi(0#) = 1 0.00/0.09 0.00/0.09 Problem 1.3: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.4: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 R0(0(x1:S)) -> R0(x1:S) 0.00/0.09 R0(1(x1:S)) -> R0(x1:S) 0.00/0.09 R0(m(x1:S)) -> R0(x1:S) 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Projection: 0.00/0.09 pi(R0) = 1 0.00/0.09 0.00/0.09 Problem 1.4: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.5: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 R1(0(x1:S)) -> R1(x1:S) 0.00/0.09 R1(1(x1:S)) -> R1(x1:S) 0.00/0.09 R1(m(x1:S)) -> R1(x1:S) 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Projection: 0.00/0.09 pi(R1) = 1 0.00/0.09 0.00/0.09 Problem 1.5: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.6: 0.00/0.09 0.00/0.09 Reduction Pair Processor: 0.00/0.09 -> Pairs: 0.00/0.09 B(ql(0(x1:S))) -> B(r0(x1:S)) 0.00/0.09 B(ql(1(x1:S))) -> B(r1(x1:S)) 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 -> Usable rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Interpretation type: 0.00/0.09 Linear 0.00/0.09 ->Coefficients: 0.00/0.09 Natural Numbers 0.00/0.09 ->Dimension: 0.00/0.09 1 0.00/0.09 ->Bound: 0.00/0.09 2 0.00/0.09 ->Interpretation: 0.00/0.09 0.00/0.09 [0](X) = X + 2 0.00/0.09 [1](X) = X + 2 0.00/0.09 [b](X) = 2.X + 2 0.00/0.09 [m](X) = 2 0.00/0.09 [r0](X) = X 0.00/0.09 [r1](X) = X + 1 0.00/0.09 [ql](X) = X 0.00/0.09 [qr](X) = 2 0.00/0.09 [B](X) = 2.X 0.00/0.09 0.00/0.09 Problem 1.6: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 B(ql(1(x1:S))) -> B(r1(x1:S)) 0.00/0.09 -> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 B(ql(1(x1:S))) -> B(r1(x1:S)) 0.00/0.09 ->->-> Rules: 0.00/0.09 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.09 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.09 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.09 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.09 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.09 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.09 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.09 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.09 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.09 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.09 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.09 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.09 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.09 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.09 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.09 0.00/0.09 Problem 1.6: 0.00/0.09 0.00/0.09 Reduction Pair Processor: 0.00/0.09 -> Pairs: 0.00/0.10 B(ql(1(x1:S))) -> B(r1(x1:S)) 0.00/0.10 -> Rules: 0.00/0.10 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.10 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.10 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.10 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.10 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.10 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.10 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.10 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.10 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.10 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.10 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.10 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.10 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.10 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.10 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.10 -> Usable rules: 0.00/0.10 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.10 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.10 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.10 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.10 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.10 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.10 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.10 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.10 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.10 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.10 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.10 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.10 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.10 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.10 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.10 ->Interpretation type: 0.00/0.10 Linear 0.00/0.10 ->Coefficients: 0.00/0.10 Natural Numbers 0.00/0.10 ->Dimension: 0.00/0.10 1 0.00/0.10 ->Bound: 0.00/0.10 2 0.00/0.10 ->Interpretation: 0.00/0.10 0.00/0.10 [0](X) = 2.X + 2 0.00/0.10 [1](X) = 2.X + 2 0.00/0.10 [b](X) = 2.X + 2 0.00/0.10 [m](X) = 2 0.00/0.10 [r0](X) = X 0.00/0.10 [r1](X) = X 0.00/0.10 [ql](X) = X 0.00/0.10 [qr](X) = 2 0.00/0.10 [B](X) = 2.X 0.00/0.10 0.00/0.10 Problem 1.6: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 0(ql(x1:S)) -> ql(0(x1:S)) 0.00/0.10 0(qr(x1:S)) -> qr(0(x1:S)) 0.00/0.10 1(ql(x1:S)) -> ql(1(x1:S)) 0.00/0.10 1(qr(x1:S)) -> qr(1(x1:S)) 0.00/0.10 b(ql(0(x1:S))) -> 0(b(r0(x1:S))) 0.00/0.10 b(ql(1(x1:S))) -> 1(b(r1(x1:S))) 0.00/0.10 m(qr(x1:S)) -> ql(m(x1:S)) 0.00/0.10 r0(0(x1:S)) -> 0(r0(x1:S)) 0.00/0.10 r0(1(x1:S)) -> 1(r0(x1:S)) 0.00/0.10 r0(b(x1:S)) -> qr(0(b(x1:S))) 0.00/0.10 r0(m(x1:S)) -> m(r0(x1:S)) 0.00/0.10 r1(0(x1:S)) -> 0(r1(x1:S)) 0.00/0.10 r1(1(x1:S)) -> 1(r1(x1:S)) 0.00/0.10 r1(b(x1:S)) -> qr(1(b(x1:S))) 0.00/0.10 r1(m(x1:S)) -> m(r1(x1:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 EOF