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TRS Innermost pair #487524018
details
property
value
status
complete
benchmark
#4.33.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.129705190659 seconds
cpu usage
0.078291436
max memory
3735552.0
stage attributes
key
value
output-size
6365
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S m:S n:S x:S y:S) (RULES sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) WEIGHT(cons(n:S,cons(m:S,x:S))) -> SUM(cons(n:S,cons(m:S,x:S)),cons(0,x:S)) WEIGHT(cons(n:S,cons(m:S,x:S))) -> WEIGHT(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) -> Rules: sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S Problem 1: SCC Processor: -> Pairs: SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) WEIGHT(cons(n:S,cons(m:S,x:S))) -> SUM(cons(n:S,cons(m:S,x:S)),cons(0,x:S)) WEIGHT(cons(n:S,cons(m:S,x:S))) -> WEIGHT(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) -> Rules: sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) ->->-> Rules: sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S ->->Cycle: ->->-> Pairs: WEIGHT(cons(n:S,cons(m:S,x:S))) -> WEIGHT(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) ->->-> Rules: sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) -> Rules: sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S -> Usable rules: Empty ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [sum](X1,X2) = 0 [weight](X) = 0 [0] = 2
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