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TRS Standard pair #516963951
details
property
value
status
complete
benchmark
rta1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.117974996567 seconds
cpu usage
0.040174008
max memory
3358720.0
stage attributes
key
value
output-size
6477
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) ) Problem 1: Dependency Pairs Processor: -> Pairs: ACK(s(x:S),0) -> ACK(x:S,s(0)) ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S) ACK(s(x:S),s(y:S)) -> ACK(x:S,plus(y:S,ack(s(x:S),y:S))) ACK(s(x:S),s(y:S)) -> PLUS(y:S,ack(s(x:S),y:S)) PLUS(s(s(x:S)),y:S) -> PLUS(x:S,s(y:S)) PLUS(x:S,s(s(y:S))) -> PLUS(s(x:S),y:S) -> Rules: ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) Problem 1: SCC Processor: -> Pairs: ACK(s(x:S),0) -> ACK(x:S,s(0)) ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S) ACK(s(x:S),s(y:S)) -> ACK(x:S,plus(y:S,ack(s(x:S),y:S))) ACK(s(x:S),s(y:S)) -> PLUS(y:S,ack(s(x:S),y:S)) PLUS(s(s(x:S)),y:S) -> PLUS(x:S,s(y:S)) PLUS(x:S,s(s(y:S))) -> PLUS(s(x:S),y:S) -> Rules: ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(s(x:S)),y:S) -> PLUS(x:S,s(y:S)) PLUS(x:S,s(s(y:S))) -> PLUS(s(x:S),y:S) ->->-> Rules: ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) ->->Cycle: ->->-> Pairs: ACK(s(x:S),0) -> ACK(x:S,s(0)) ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S) ACK(s(x:S),s(y:S)) -> ACK(x:S,plus(y:S,ack(s(x:S),y:S))) ->->-> Rules: ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pair Processor: -> Pairs: PLUS(s(s(x:S)),y:S) -> PLUS(x:S,s(y:S)) PLUS(x:S,s(s(y:S))) -> PLUS(s(x:S),y:S) -> Rules: ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S)
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