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TRS_Conditional 2019-03-28 22.59 pair #432272530
details
property
value
status
complete
benchmark
292.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0207561 seconds
cpu usage
0.021296
user time
0.009059
system time
0.012237
max virtual memory
113176.0
max residence set size
6912.0
stage attributes
key
value
starexec-result
YES
output
0.00/0.01 YES 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 (VAR v_NonEmpty:S l:S x:S y:S) 0.00/0.01 (RULES 0.00/0.01 le(0,s(x:S)) -> ttrue 0.00/0.01 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.00/0.01 le(x:S,0) -> ffalse 0.00/0.01 min(cons(x:S,nil)) -> x:S 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S 0.00/0.01 min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue 0.00/0.01 ) 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 Valid CTRS Processor: 0.00/0.01 -> Rules: 0.00/0.01 le(0,s(x:S)) -> ttrue 0.00/0.01 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.00/0.01 le(x:S,0) -> ffalse 0.00/0.01 min(cons(x:S,nil)) -> x:S 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S 0.00/0.01 min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue 0.00/0.01 -> The system is a deterministic 3-CTRS. 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 Dependency Pairs Processor: 0.00/0.01 0.00/0.01 Conditional Termination Problem 1: 0.00/0.01 -> Pairs: 0.00/0.01 LE(s(x:S),s(y:S)) -> LE(x:S,y:S) 0.00/0.01 MIN(cons(x:S,l:S)) -> MIN(l:S) | le(x:S,min(l:S)) ->* ffalse 0.00/0.01 MIN(cons(x:S,l:S)) -> MIN(l:S) | min(l:S) ->* x:S 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 le(0,s(x:S)) -> ttrue 0.00/0.01 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.00/0.01 le(x:S,0) -> ffalse 0.00/0.01 min(cons(x:S,nil)) -> x:S 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S 0.00/0.01 min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue 0.00/0.01 0.00/0.01 Conditional Termination Problem 2: 0.00/0.01 -> Pairs: 0.00/0.01 MIN(cons(x:S,l:S)) -> LE(x:S,min(l:S)) 0.00/0.01 MIN(cons(x:S,l:S)) -> MIN(l:S) 0.00/0.01 -> QPairs: 0.00/0.01 LE(s(x:S),s(y:S)) -> LE(x:S,y:S) 0.00/0.01 MIN(cons(x:S,l:S)) -> MIN(l:S) | le(x:S,min(l:S)) ->* ffalse 0.00/0.01 MIN(cons(x:S,l:S)) -> MIN(l:S) | min(l:S) ->* x:S 0.00/0.01 -> Rules: 0.00/0.01 le(0,s(x:S)) -> ttrue 0.00/0.01 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.00/0.01 le(x:S,0) -> ffalse 0.00/0.01 min(cons(x:S,nil)) -> x:S 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S 0.00/0.01 min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue 0.00/0.01 0.00/0.01 0.00/0.01 The problem is decomposed in 2 subproblems. 0.00/0.01 0.00/0.01 Problem 1.1: 0.00/0.01 0.00/0.01 SCC Processor: 0.00/0.01 -> Pairs: 0.00/0.01 LE(s(x:S),s(y:S)) -> LE(x:S,y:S) 0.00/0.01 MIN(cons(x:S,l:S)) -> MIN(l:S) | le(x:S,min(l:S)) ->* ffalse 0.00/0.01 MIN(cons(x:S,l:S)) -> MIN(l:S) | min(l:S) ->* x:S 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 le(0,s(x:S)) -> ttrue 0.00/0.01 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.00/0.01 le(x:S,0) -> ffalse 0.00/0.01 min(cons(x:S,nil)) -> x:S 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S 0.00/0.01 min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue 0.00/0.01 ->Strongly Connected Components: 0.00/0.01 ->->Cycle: 0.00/0.01 ->->-> Pairs: 0.00/0.01 MIN(cons(x:S,l:S)) -> MIN(l:S) | le(x:S,min(l:S)) ->* ffalse 0.00/0.01 MIN(cons(x:S,l:S)) -> MIN(l:S) | min(l:S) ->* x:S 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 ->->-> Rules: 0.00/0.01 le(0,s(x:S)) -> ttrue 0.00/0.01 le(s(x:S),s(y:S)) -> le(x:S,y:S) 0.00/0.01 le(x:S,0) -> ffalse 0.00/0.01 min(cons(x:S,nil)) -> x:S 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse 0.00/0.01 min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S 0.00/0.01 min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue 0.00/0.01 ->->Cycle:
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