details

property	value
status	complete
benchmark	378.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n157.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	20.0965 seconds
cpu usage	20.0974
user time	19.2839
system time	0.813472
max virtual memory	598012.0
max residence set size	8372.0

stage attributes

key	value
starexec-result	YES

output

19.98/20.08 YES 19.98/20.08 19.98/20.08 Problem 1: 19.98/20.08 19.98/20.08 (VAR v_NonEmpty:S rest:S x:S y:S z1:S z2:S) 19.98/20.08 (RULES 19.98/20.08 cons(x:S,cons(x:S,rest:S)) -> cons(x:S,rest:S) 19.98/20.08 cons(x:S,cons(y:S,rest:S)) -> cons(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 orient(s(x:S),0) -> pair(0,s(x:S)) 19.98/20.08 orient(s(x:S),s(y:S)) -> pair(s(z1:S),s(z2:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 ) 19.98/20.08 19.98/20.08 Problem 1: 19.98/20.08 Valid CTRS Processor: 19.98/20.08 -> Rules: 19.98/20.08 cons(x:S,cons(x:S,rest:S)) -> cons(x:S,rest:S) 19.98/20.08 cons(x:S,cons(y:S,rest:S)) -> cons(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 orient(s(x:S),0) -> pair(0,s(x:S)) 19.98/20.08 orient(s(x:S),s(y:S)) -> pair(s(z1:S),s(z2:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 -> The system is a deterministic 3-CTRS. 19.98/20.08 19.98/20.08 Problem 1: 19.98/20.08 19.98/20.08 Dependency Pairs Processor: 19.98/20.08 19.98/20.08 Conditional Termination Problem 1: 19.98/20.08 -> Pairs: 19.98/20.08 CONS(x:S,cons(y:S,rest:S)) -> CONS(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 CONS(x:S,cons(y:S,rest:S)) -> CONS(z2:S,rest:S) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 -> QPairs: 19.98/20.08 Empty 19.98/20.08 -> Rules: 19.98/20.08 cons(x:S,cons(x:S,rest:S)) -> cons(x:S,rest:S) 19.98/20.08 cons(x:S,cons(y:S,rest:S)) -> cons(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 orient(s(x:S),0) -> pair(0,s(x:S)) 19.98/20.08 orient(s(x:S),s(y:S)) -> pair(s(z1:S),s(z2:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 19.98/20.08 Conditional Termination Problem 2: 19.98/20.08 -> Pairs: 19.98/20.08 CONS(x:S,cons(y:S,rest:S)) -> ORIENT(x:S,y:S) 19.98/20.08 ORIENT(s(x:S),s(y:S)) -> ORIENT(x:S,y:S) 19.98/20.08 -> QPairs: 19.98/20.08 Empty 19.98/20.08 -> Rules: 19.98/20.08 cons(x:S,cons(x:S,rest:S)) -> cons(x:S,rest:S) 19.98/20.08 cons(x:S,cons(y:S,rest:S)) -> cons(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 orient(s(x:S),0) -> pair(0,s(x:S)) 19.98/20.08 orient(s(x:S),s(y:S)) -> pair(s(z1:S),s(z2:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 19.98/20.08 19.98/20.08 The problem is decomposed in 2 subproblems. 19.98/20.08 19.98/20.08 Problem 1.1: 19.98/20.08 19.98/20.08 SCC Processor: 19.98/20.08 -> Pairs: 19.98/20.08 CONS(x:S,cons(y:S,rest:S)) -> CONS(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 CONS(x:S,cons(y:S,rest:S)) -> CONS(z2:S,rest:S) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 -> QPairs: 19.98/20.08 Empty 19.98/20.08 -> Rules: 19.98/20.08 cons(x:S,cons(x:S,rest:S)) -> cons(x:S,rest:S) 19.98/20.08 cons(x:S,cons(y:S,rest:S)) -> cons(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 orient(s(x:S),0) -> pair(0,s(x:S)) 19.98/20.08 orient(s(x:S),s(y:S)) -> pair(s(z1:S),s(z2:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 ->Strongly Connected Components: 19.98/20.08 ->->Cycle: 19.98/20.08 ->->-> Pairs: 19.98/20.08 CONS(x:S,cons(y:S,rest:S)) -> CONS(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 CONS(x:S,cons(y:S,rest:S)) -> CONS(z2:S,rest:S) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 -> QPairs: 19.98/20.08 Empty 19.98/20.08 ->->-> Rules: 19.98/20.08 cons(x:S,cons(x:S,rest:S)) -> cons(x:S,rest:S) 19.98/20.08 cons(x:S,cons(y:S,rest:S)) -> cons(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 orient(s(x:S),0) -> pair(0,s(x:S)) 19.98/20.08 orient(s(x:S),s(y:S)) -> pair(s(z1:S),s(z2:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 19.98/20.08 Problem 1.1: 19.98/20.08 19.98/20.08 Reduction Triple Processor: 19.98/20.08 -> Pairs: 19.98/20.08 CONS(x:S,cons(y:S,rest:S)) -> CONS(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 CONS(x:S,cons(y:S,rest:S)) -> CONS(z2:S,rest:S) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 -> QPairs: 19.98/20.08 Empty 19.98/20.08 -> Rules: 19.98/20.08 cons(x:S,cons(x:S,rest:S)) -> cons(x:S,rest:S) 19.98/20.08 cons(x:S,cons(y:S,rest:S)) -> cons(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 orient(s(x:S),0) -> pair(0,s(x:S)) 19.98/20.08 orient(s(x:S),s(y:S)) -> pair(s(z1:S),s(z2:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 -> Usable rules: 19.98/20.08 cons(x:S,cons(x:S,rest:S)) -> cons(x:S,rest:S) 19.98/20.08 cons(x:S,cons(y:S,rest:S)) -> cons(z1:S,cons(z2:S,rest:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 orient(s(x:S),0) -> pair(0,s(x:S)) 19.98/20.08 orient(s(x:S),s(y:S)) -> pair(s(z1:S),s(z2:S)) | orient(x:S,y:S) ->* pair(z1:S,z2:S) 19.98/20.08 ->Interpretation type: 19.98/20.08 Linear 19.98/20.08 ->Coefficients: 19.98/20.08 Natural Numbers popout

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actions

all output return to TRS_Conditional 2019-03-28 22.59