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TRS_Conditional 2019-03-28 22.59 pair #432272496
details
property
value
status
complete
benchmark
353.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n039.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
170.498 seconds
cpu usage
170.27
user time
163.42
system time
6.85
max virtual memory
1242352.0
max residence set size
143732.0
stage attributes
key
value
starexec-result
YES
output
170.27/170.49 YES 170.27/170.49 170.27/170.49 Problem 1: 170.27/170.49 170.27/170.49 (VAR v_NonEmpty:S v:S w:S ws:S x':S xs:S xs':S y:S y':S ys:S ys':S z:S zs:S) 170.27/170.49 (RULES 170.27/170.49 get(cons(x':S,xs':S)) -> tp2(y:S,cons(x':S,zs:S)) | get(xs':S) ->* tp2(y:S,zs:S) 170.27/170.49 get(cons(y:S,ys:S)) -> tp2(y:S,ys:S) 170.27/170.49 ssp'(cons(x':S,xs':S),v:S) -> cons(y':S,ys':S) | get(xs':S) ->* tp2(y':S,zs:S), sub(v:S,y':S) ->* w:S, ssp'(cons(x':S,zs:S),w:S) ->* ys':S 170.27/170.49 ssp'(cons(y':S,ws:S),v:S) -> cons(y':S,ys':S) | sub(v:S,y':S) ->* w:S, ssp'(ws:S,w:S) ->* ys':S 170.27/170.49 ssp'(xs:S,0) -> nil 170.27/170.49 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S 170.27/170.49 sub(z:S,0) -> z:S 170.27/170.49 ) 170.27/170.49 170.27/170.49 Problem 1: 170.27/170.49 Valid CTRS Processor: 170.27/170.49 -> Rules: 170.27/170.49 get(cons(x':S,xs':S)) -> tp2(y:S,cons(x':S,zs:S)) | get(xs':S) ->* tp2(y:S,zs:S) 170.27/170.49 get(cons(y:S,ys:S)) -> tp2(y:S,ys:S) 170.27/170.49 ssp'(cons(x':S,xs':S),v:S) -> cons(y':S,ys':S) | get(xs':S) ->* tp2(y':S,zs:S), sub(v:S,y':S) ->* w:S, ssp'(cons(x':S,zs:S),w:S) ->* ys':S 170.27/170.49 ssp'(cons(y':S,ws:S),v:S) -> cons(y':S,ys':S) | sub(v:S,y':S) ->* w:S, ssp'(ws:S,w:S) ->* ys':S 170.27/170.49 ssp'(xs:S,0) -> nil 170.27/170.49 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S 170.27/170.49 sub(z:S,0) -> z:S 170.27/170.49 -> The system is a deterministic 3-CTRS. 170.27/170.49 170.27/170.49 Problem 1: 170.27/170.49 170.27/170.49 Dependency Pairs Processor: 170.27/170.49 170.27/170.49 Conditional Termination Problem 1: 170.27/170.49 -> Pairs: 170.27/170.49 Empty 170.27/170.49 -> QPairs: 170.27/170.49 Empty 170.27/170.49 -> Rules: 170.27/170.49 get(cons(x':S,xs':S)) -> tp2(y:S,cons(x':S,zs:S)) | get(xs':S) ->* tp2(y:S,zs:S) 170.27/170.49 get(cons(y:S,ys:S)) -> tp2(y:S,ys:S) 170.27/170.49 ssp'(cons(x':S,xs':S),v:S) -> cons(y':S,ys':S) | get(xs':S) ->* tp2(y':S,zs:S), sub(v:S,y':S) ->* w:S, ssp'(cons(x':S,zs:S),w:S) ->* ys':S 170.27/170.49 ssp'(cons(y':S,ws:S),v:S) -> cons(y':S,ys':S) | sub(v:S,y':S) ->* w:S, ssp'(ws:S,w:S) ->* ys':S 170.27/170.49 ssp'(xs:S,0) -> nil 170.27/170.49 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S 170.27/170.49 sub(z:S,0) -> z:S 170.27/170.49 170.27/170.49 Conditional Termination Problem 2: 170.27/170.49 -> Pairs: 170.27/170.49 GET(cons(x':S,xs':S)) -> GET(xs':S) 170.27/170.49 SSP'(cons(x':S,xs':S),v:S) -> GET(xs':S) 170.27/170.49 SSP'(cons(x':S,xs':S),v:S) -> SSP'(cons(x':S,zs:S),w:S) | get(xs':S) ->* tp2(y':S,zs:S), sub(v:S,y':S) ->* w:S 170.27/170.49 SSP'(cons(x':S,xs':S),v:S) -> SUB(v:S,y':S) | get(xs':S) ->* tp2(y':S,zs:S) 170.27/170.49 SSP'(cons(y':S,ws:S),v:S) -> SSP'(ws:S,w:S) | sub(v:S,y':S) ->* w:S 170.27/170.49 SSP'(cons(y':S,ws:S),v:S) -> SUB(v:S,y':S) 170.27/170.49 SUB(s(v:S),s(w:S)) -> SUB(v:S,w:S) 170.27/170.49 -> QPairs: 170.27/170.49 Empty 170.27/170.49 -> Rules: 170.27/170.49 get(cons(x':S,xs':S)) -> tp2(y:S,cons(x':S,zs:S)) | get(xs':S) ->* tp2(y:S,zs:S) 170.27/170.49 get(cons(y:S,ys:S)) -> tp2(y:S,ys:S) 170.27/170.49 ssp'(cons(x':S,xs':S),v:S) -> cons(y':S,ys':S) | get(xs':S) ->* tp2(y':S,zs:S), sub(v:S,y':S) ->* w:S, ssp'(cons(x':S,zs:S),w:S) ->* ys':S 170.27/170.49 ssp'(cons(y':S,ws:S),v:S) -> cons(y':S,ys':S) | sub(v:S,y':S) ->* w:S, ssp'(ws:S,w:S) ->* ys':S 170.27/170.49 ssp'(xs:S,0) -> nil 170.27/170.49 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S 170.27/170.49 sub(z:S,0) -> z:S 170.27/170.49 170.27/170.49 170.27/170.49 The problem is decomposed in 2 subproblems. 170.27/170.49 170.27/170.49 Problem 1.1: 170.27/170.49 170.27/170.49 SCC Processor: 170.27/170.49 -> Pairs: 170.27/170.49 Empty 170.27/170.49 -> QPairs: 170.27/170.49 Empty 170.27/170.49 -> Rules: 170.27/170.49 get(cons(x':S,xs':S)) -> tp2(y:S,cons(x':S,zs:S)) | get(xs':S) ->* tp2(y:S,zs:S) 170.27/170.49 get(cons(y:S,ys:S)) -> tp2(y:S,ys:S) 170.27/170.49 ssp'(cons(x':S,xs':S),v:S) -> cons(y':S,ys':S) | get(xs':S) ->* tp2(y':S,zs:S), sub(v:S,y':S) ->* w:S, ssp'(cons(x':S,zs:S),w:S) ->* ys':S 170.27/170.49 ssp'(cons(y':S,ws:S),v:S) -> cons(y':S,ys':S) | sub(v:S,y':S) ->* w:S, ssp'(ws:S,w:S) ->* ys':S 170.27/170.49 ssp'(xs:S,0) -> nil 170.27/170.49 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S 170.27/170.49 sub(z:S,0) -> z:S 170.27/170.49 ->Strongly Connected Components: 170.27/170.49 There is no strongly connected component 170.27/170.49 170.27/170.49 The problem is finite. 170.27/170.49 170.27/170.49 Problem 1.2: 170.27/170.49 170.27/170.49 SCC Processor: 170.27/170.49 -> Pairs: 170.27/170.49 GET(cons(x':S,xs':S)) -> GET(xs':S) 170.27/170.49 SSP'(cons(x':S,xs':S),v:S) -> GET(xs':S) 170.27/170.49 SSP'(cons(x':S,xs':S),v:S) -> SSP'(cons(x':S,zs:S),w:S) | get(xs':S) ->* tp2(y':S,zs:S), sub(v:S,y':S) ->* w:S 170.27/170.49 SSP'(cons(x':S,xs':S),v:S) -> SUB(v:S,y':S) | get(xs':S) ->* tp2(y':S,zs:S) 170.27/170.49 SSP'(cons(y':S,ws:S),v:S) -> SSP'(ws:S,w:S) | sub(v:S,y':S) ->* w:S 170.27/170.49 SSP'(cons(y':S,ws:S),v:S) -> SUB(v:S,y':S) 170.27/170.49 SUB(s(v:S),s(w:S)) -> SUB(v:S,w:S) 170.27/170.49 -> QPairs:
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