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 y) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (le 1, 2) 0.001/0.001 (m) 0.001/0.001 (pop 1) 0.001/0.001 (size 1) 0.001/0.001 (top 1) 0.001/0.001 (0) 0.001/0.001 (eentry) 0.001/0.001 (empty) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (push 1, 2) 0.001/0.001 (s 1) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 le(0,s(x)) -> true 0.001/0.001 le(s(x),s(y)) -> le(x,y) 0.001/0.001 le(x,0) -> false 0.001/0.001 m -> s(s(s(s(0)))) 0.001/0.001 pop(empty) -> empty 0.001/0.001 pop(push(x,y)) -> x | le(size(x),m) ->* true 0.001/0.001 size(empty) -> 0 0.001/0.001 size(push(x,y)) -> s(size(x)) 0.001/0.001 top(empty) -> eentry 0.001/0.001 top(push(x,y)) -> y | le(size(x),m) ->* 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 y) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (le 1, 2) 0.001/0.001 (m) 0.001/0.001 (pop 1) 0.001/0.001 (size 1) 0.001/0.001 (top 1) 0.001/0.001 (0) 0.001/0.001 (eentry) 0.001/0.001 (empty) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (push 1, 2) 0.001/0.001 (s 1) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 le(0,s(x)) -> true 0.001/0.001 le(s(x),s(y)) -> le(x,y) 0.001/0.001 le(x,0) -> false 0.001/0.001 m -> s(s(s(s(0)))) 0.001/0.001 pop(empty) -> empty 0.001/0.001 pop(push(x,y)) -> x | le(size(x),m) ->* true 0.001/0.001 size(empty) -> 0 0.001/0.001 size(push(x,y)) -> s(size(x)) 0.001/0.001 top(empty) -> eentry 0.001/0.001 top(push(x,y)) -> y | le(size(x),m) ->* 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 y) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (le 1, 2) 0.001/0.001 (m) 0.001/0.001 (pop 1) 0.001/0.001 (size 1) 0.001/0.001 (top 1) 0.001/0.001 (0) 0.001/0.001 (eentry) 0.001/0.001 (empty) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (push 1, 2) 0.001/0.001 (s 1) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 le(0,s(x)) -> true 0.001/0.001 le(s(x),s(y)) -> le(x,y) 0.001/0.001 le(x,0) -> false 0.001/0.001 m -> s(s(s(s(0)))) 0.001/0.001 pop(empty) -> empty 0.001/0.001 pop(push(x,y)) -> x | le(size(x),m) ->* true 0.001/0.001 size(empty) -> 0 0.001/0.001 size(push(x,y)) -> s(size(x)) 0.001/0.001 top(empty) -> eentry 0.001/0.001 top(push(x,y)) -> y | le(size(x),m) ->* 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 le(0,s(x)) -> true 0.001/0.001 le(s(x),s(y)) -> le(x,y) 0.001/0.001 le(x,0) -> false 0.001/0.001 m -> s(s(s(s(0)))) 0.001/0.001 pop(empty) -> empty 0.001/0.001 pop(push(x,y)) -> x | le(size(x),m) ->* true 0.001/0.001 size(empty) -> 0 0.001/0.001 size(push(x,y)) -> s(size(x)) 0.001/0.001 top(empty) -> eentry 0.001/0.001 top(push(x,y)) -> y | le(size(x),m) ->* true 0.001/0.001 -> Vars: 0.001/0.001 "x", "y" 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 crule: le(0,s(x)) -> true, id: 1, possubterms: le(0,s(x))-> [], 0-> [1], s(x)-> [2] 0.001/0.001 crule: le(s(x),s(y)) -> le(x,y), id: 2, possubterms: le(s(x),s(y))-> [], s(x)-> [1], s(y)-> [2] 0.001/0.001 crule: le(x,0) -> false, id: 3, possubterms: le(x,0)-> [], 0-> [2] 0.001/0.001 crule: m -> s(s(s(s(0)))), id: 4, possubterms: m-> [] 0.001/0.001 crule: pop(empty) -> empty, id: 5, possubterms: pop(empty)-> [], empty-> [1] 0.001/0.001 crule: pop(push(x,y)) -> x | le(size(x),m) ->* true, id: 6, possubterms: pop(push(x,y))-> [], push(x,y)-> [1] 0.001/0.001 crule: size(empty) -> 0, id: 7, possubterms: size(empty)-> [], empty-> [1] 0.001/0.001 crule: size(push(x,y)) -> s(size(x)), id: 8, possubterms: size(push(x,y))-> [], push(x,y)-> [1] 0.001/0.001 crule: top(empty) -> eentry, id: 9, possubterms: top(empty)-> [], empty-> [1] 0.001/0.001 crule: top(push(x,y)) -> y | le(size(x),m) ->* true, id: 10, possubterms: top(push(x,y))-> [], push(x,y)-> [1] 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 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 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 y) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (le 1, 2) 0.001/0.001 (m) 0.001/0.001 (pop 1) 0.001/0.001 (size 1) 0.001/0.001 (top 1) 0.001/0.001 (0) 0.001/0.001 (eentry) 0.001/0.001 (empty) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (push 1, 2) 0.001/0.001 (s 1) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 le(0,s(x)) -> true 0.001/0.001 le(s(x),s(y)) -> le(x,y) 0.001/0.001 le(x,0) -> false 0.001/0.001 m -> s(s(s(s(0)))) 0.001/0.001 pop(empty) -> empty 0.001/0.001 pop(push(x,y)) -> x | le(size(x),m) ->* true 0.001/0.001 size(empty) -> 0 0.001/0.001 size(push(x,y)) -> s(size(x)) 0.001/0.001 top(empty) -> eentry 0.001/0.001 top(push(x,y)) -> y | le(size(x),m) ->* 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: 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 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 46%CPU (0avgtext+0avgdata 8668maxresident)k 0.001/0.001 8inputs+0outputs (0major+765minor)pagefaults 0swaps