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 z) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (f 1) 0.001/0.001 (h 1, 2) 0.001/0.001 (a) 0.001/0.001 (b) 0.001/0.001 (c) 0.001/0.001 (d) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (g 1, 2, 3) 0.001/0.001 (i 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f(x) -> g(x,y,z) | h(a,x) ->* i(y), h(a,y) ->* i(z) 0.001/0.001 h(a,a) -> i(b) 0.001/0.001 h(a,b) -> i(c) 0.001/0.001 h(b,b) -> i(d) 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 z) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (f 1) 0.001/0.001 (h 1, 2) 0.001/0.001 (a) 0.001/0.001 (b) 0.001/0.001 (c) 0.001/0.001 (d) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (g 1, 2, 3) 0.001/0.001 (i 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f(x) -> g(x,y,z) | h(a,x) ->* i(y), h(a,y) ->* i(z) 0.001/0.001 h(a,a) -> i(b) 0.001/0.001 h(a,b) -> i(c) 0.001/0.001 h(b,b) -> i(d) 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 z) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (f 1) 0.001/0.001 (h 1, 2) 0.001/0.001 (a) 0.001/0.001 (b) 0.001/0.001 (c) 0.001/0.001 (d) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (g 1, 2, 3) 0.001/0.001 (i 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f(x) -> g(x,y,z) | h(a,x) ->* i(y), h(a,y) ->* i(z) 0.001/0.001 h(a,a) -> i(b) 0.001/0.001 h(a,b) -> i(c) 0.001/0.001 h(b,b) -> i(d) 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 f(x) -> g(x,y,z) | h(a,x) ->* i(y), h(a,y) ->* i(z) 0.001/0.001 h(a,a) -> i(b) 0.001/0.001 h(a,b) -> i(c) 0.001/0.001 h(b,b) -> i(d) 0.001/0.001 -> Vars: 0.001/0.001 "x", "y", "z" 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 crule: f(x) -> g(x,y,z) | h(a,x) ->* i(y), h(a,y) ->* i(z), id: 1, possubterms: f(x)-> [] 0.001/0.001 crule: h(a,a) -> i(b), id: 2, possubterms: h(a,a)-> [], a-> [1], a-> [2] 0.001/0.001 crule: h(a,b) -> i(c), id: 3, possubterms: h(a,b)-> [], a-> [1], b-> [2] 0.001/0.001 crule: h(b,b) -> i(d), id: 4, possubterms: h(b,b)-> [], b-> [1], b-> [2] 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: 3 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 z) 0.001/0.001 (REPLACEMENT-MAP 0.001/0.001 (f 1) 0.001/0.001 (h 1, 2) 0.001/0.001 (a) 0.001/0.001 (b) 0.001/0.001 (c) 0.001/0.001 (d) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (g 1, 2, 3) 0.001/0.001 (i 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f(x) -> g(x,y,z) | h(a,x) ->* i(y), h(a,y) ->* i(z) 0.001/0.001 h(a,a) -> i(b) 0.001/0.001 h(a,b) -> i(c) 0.001/0.001 h(b,b) -> i(d) 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: i(c_y) 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: i(c_z) 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: 3 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 38%CPU (0avgtext+0avgdata 8276maxresident)k 0.001/0.001 8inputs+0outputs (0major+728minor)pagefaults 0swaps