0.001/0.001 YES 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty x) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (pos 1) 0.001/0.001 (0) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (p 1) 0.001/0.001 (s 1) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 pos(0) -> false 0.001/0.001 pos(p(x)) -> false | pos(x) ->* false 0.001/0.001 pos(s(0)) -> true 0.001/0.001 pos(s(x)) -> true | pos(x) ->* true 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 Inlining of Conditions Processor [STERN17]: 0.001/0.001 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty x) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (pos 1) 0.001/0.001 (0) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (p 1) 0.001/0.001 (s 1) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 pos(0) -> false 0.001/0.001 pos(p(x)) -> false | pos(x) ->* false 0.001/0.001 pos(s(0)) -> true 0.001/0.001 pos(s(x)) -> true | pos(x) ->* true 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty x) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (pos 1) 0.001/0.001 (0) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (p 1) 0.001/0.001 (s 1) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 pos(0) -> false 0.001/0.001 pos(p(x)) -> false | pos(x) ->* false 0.001/0.001 pos(s(0)) -> true 0.001/0.001 pos(s(x)) -> true | pos(x) ->* true 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Critical Pairs Processor: 0.001/0.001 -> Rules: 0.001/0.001 pos(0) -> false 0.001/0.001 pos(p(x)) -> false | pos(x) ->* false 0.001/0.001 pos(s(0)) -> true 0.001/0.001 pos(s(x)) -> true | pos(x) ->* true 0.001/0.001 -> Vars: 0.001/0.001 "x" 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 crule: pos(0) -> false, id: 1, possubterms: pos(0)-> [], 0-> [1] 0.001/0.001 crule: pos(p(x)) -> false | pos(x) ->* false, id: 2, possubterms: pos(p(x))-> [], p(x)-> [1] 0.001/0.001 crule: pos(s(0)) -> true, id: 3, possubterms: pos(s(0))-> [], s(0)-> [1], 0-> [1,1] 0.001/0.001 crule: pos(s(x)) -> true | pos(x) ->* true, id: 4, possubterms: pos(s(x))-> [], s(x)-> [1] 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 R4 unifies with R3 at p: [], l: pos(s(x)), lp: pos(s(x)), conds: {pos(x) ->* true}, sig: {x -> 0}, l': pos(s(0)), r: true, r': true 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 | pos(0) ->* true => Trivial, Overlay, NW2, N1 0.001/0.001 0.001/0.001 -> Problem conclusions: 0.001/0.001 Left linear, Right linear, Linear 0.001/0.001 Weakly orthogonal, Almost orthogonal, Not orthogonal 0.001/0.001 CTRS Type: 1 0.001/0.001 Deterministic, Strongly deterministic 0.001/0.001 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 0.001/0.001 Maybe right-stable CTRS, Overlay CTRS 0.001/0.001 Maybe normal CTRS, Maybe almost normal CTRS 0.001/0.001 Maybe terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 0.001/0.001 Maybe level confluent 0.001/0.001 Maybe confluent 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR x) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (pos 1) 0.001/0.001 (0) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (p 1) 0.001/0.001 (s 1) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 pos(0) -> false 0.001/0.001 pos(p(x)) -> false | pos(x) ->* false 0.001/0.001 pos(s(0)) -> true 0.001/0.001 pos(s(x)) -> true | pos(x) ->* true 0.001/0.001 ) 0.001/0.001 Critical Pairs: 0.001/0.001 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Right Stable Processor: 0.001/0.001 Right-stable CTRS 0.001/0.001 Justification: 0.001/0.001 0.001/0.001 -> Term right-stability conditions: 0.001/0.001 Term: false 0.001/0.001 Right-stable term 0.001/0.001 Linear constructor form 0.001/0.001 Don't know if term is a ground normal form (not needed) 0.001/0.001 Right-stability condition achieved 0.001/0.001 A call to InfChecker wasn't needed 0.001/0.001 0.001/0.001 0.001/0.001 -> Term right-stability conditions: 0.001/0.001 Term: true 0.001/0.001 Right-stable term 0.001/0.001 Linear constructor form 0.001/0.001 Don't know if term is a ground normal form (not needed) 0.001/0.001 Right-stability condition achieved 0.001/0.001 A call to InfChecker wasn't needed 0.001/0.001 0.001/0.001 -> Problem conclusions: 0.001/0.001 Left linear, Right linear, Linear 0.001/0.001 Weakly orthogonal, Almost orthogonal, Orthogonal 0.001/0.001 CTRS Type: 1 0.001/0.001 Deterministic, Strongly deterministic 0.001/0.001 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 0.001/0.001 Right-stable CTRS, Overlay CTRS 0.001/0.001 Maybe normal CTRS, Almost normal CTRS 0.001/0.001 Maybe terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 0.001/0.001 Level confluent 0.001/0.001 Confluent 0.001/0.001 0.001/0.001 The problem is joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 41%CPU (0avgtext+0avgdata 8412maxresident)k 0.001/0.001 8inputs+0outputs (0major+740minor)pagefaults 0swaps