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:S x:S y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 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:S)) -> true 0.001/0.001 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.001/0.001 le(x:S,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:S,y:S)) -> x:S | le(size(x:S),m) ->* true 0.001/0.001 size(empty) -> 0 0.001/0.001 size(push(x:S,y:S)) -> s(size(x:S)) 0.001/0.001 top(empty) -> eentry 0.001/0.001 top(push(x:S,y:S)) -> y:S | le(size(x:S),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:S x:S y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 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:S)) -> true 0.001/0.001 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.001/0.001 le(x:S,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:S,y:S)) -> x:S | le(size(x:S),m) ->* true 0.001/0.001 size(empty) -> 0 0.001/0.001 size(push(x:S,y:S)) -> s(size(x:S)) 0.001/0.001 top(empty) -> eentry 0.001/0.001 top(push(x:S,y:S)) -> y:S | le(size(x:S),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:S x:S y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 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:S)) -> true 0.001/0.001 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.001/0.001 le(x:S,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:S,y:S)) -> x:S | le(size(x:S),m) ->* true 0.001/0.001 size(empty) -> 0 0.001/0.001 size(push(x:S,y:S)) -> s(size(x:S)) 0.001/0.001 top(empty) -> eentry 0.001/0.001 top(push(x:S,y:S)) -> y:S | le(size(x:S),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:S)) -> true 0.001/0.001 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.001/0.001 le(x:S,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:S,y:S)) -> x:S | le(size(x:S),m) ->* true 0.001/0.001 size(empty) -> 0 0.001/0.001 size(push(x:S,y:S)) -> s(size(x:S)) 0.001/0.001 top(empty) -> eentry 0.001/0.001 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* true 0.001/0.001 -> Vars: 0.001/0.001 "x", "x", "y", "x", "x", "y", "x", "y", "x", "y" 0.001/0.001 -> FVars: 0.001/0.001 "x3", "x4", "x5", "x6", "x7", "x8", "x9", "x10", "x11", "x12" 0.001/0.001 -> PVars: 0.001/0.001 "x": ["x3", "x4", "x6", "x7", "x9", "x11"], "y": ["x5", "x8", "x10", "x12"] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 crule: le(0,s(x3:S)) -> true, id: 1, possubterms: le(0,s(x3:S))-> [], 0-> [1], s(x3:S)-> [2] 0.001/0.001 crule: le(s(x4:S),s(x5:S)) -> le(x4:S,x5:S), id: 2, possubterms: le(s(x4:S),s(x5:S))-> [], s(x4:S)-> [1], s(x5:S)-> [2] 0.001/0.001 crule: le(x6:S,0) -> false, id: 3, possubterms: le(x6:S,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(x7:S,x8:S)) -> x7:S | le(size(x7:S),m) ->* true, id: 6, possubterms: pop(push(x7:S,x8:S))-> [], push(x7:S,x8:S)-> [1] 0.001/0.001 crule: size(empty) -> 0, id: 7, possubterms: size(empty)-> [], empty-> [1] 0.001/0.001 crule: size(push(x9:S,x10:S)) -> s(size(x9:S)), id: 8, possubterms: size(push(x9:S,x10:S))-> [], push(x9:S,x10:S)-> [1] 0.001/0.001 crule: top(empty) -> eentry, id: 9, possubterms: top(empty)-> [], empty-> [1] 0.001/0.001 crule: top(push(x11:S,x12:S)) -> x12:S | le(size(x11:S),m) ->* true, id: 10, possubterms: top(push(x11:S,x12:S))-> [], push(x11:S,x12:S)-> [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 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, 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 vNonEmpty:S x:S y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 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:S)) -> true 0.001/0.001 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.001/0.001 le(x:S,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:S,y:S)) -> x:S | le(size(x:S),m) ->* true 0.001/0.001 size(empty) -> 0 0.001/0.001 size(push(x:S,y:S)) -> s(size(x:S)) 0.001/0.001 top(empty) -> eentry 0.001/0.001 top(push(x:S,y:S)) -> y:S | le(size(x:S),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 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, 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 58%CPU (0avgtext+0avgdata 8632maxresident)k 0.001/0.001 8inputs+0outputs (0major+699minor)pagefaults 0swaps