Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Derivational Complexity: TRS pair #487103380
details
property
value
status
complete
benchmark
4206.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
ICFP_2010
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
296.679 seconds
cpu usage
1123.01
user time
1119.06
system time
3.95316
max virtual memory
1.8755976E7
max residence set size
6130508.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 55 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 234 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(0(1(2(3(1(4(4(1(0(5(4(4(2(3(5(5(3(2(3(4(0(4(0(4(3(5(4(2(4(0(1(4(2(1(1(2(4(4(4(0(2(5(1(3(0(0(0(2(4(3(2(1(4(1(4(5(2(4(0(2(5(1(2(3(3(4(5(0(0(0(1(1(0(0(4(3(4(4(3(0(3(5(0(4(3(2(5(2(3(2(4(1(4(5(5(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(2(3(5(1(0(3(1(0(5(1(5(1(5(2(2(2(1(4(1(4(1(3(0(1(0(4(0(3(3(4(5(5(5(1(5(4(3(5(1(4(0(5(5(3(3(3(4(4(0(5(2(3(5(1(3(2(3(4(5(4(2(5(4(0(0(3(2(3(4(4(0(4(2(0(1(3(3(5(2(2(4(0(1(4(3(2(4(1(4(0(1(3(1(3(4(3(2(0(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(2(3(1(5(1(5(5(2(0(0(0(3(0(2(2(5(5(5(0(1(0(1(3(3(1(4(4(1(2(3(5(1(3(2(1(2(2(4(5(1(3(4(1(0(3(1(2(4(2(4(1(1(4(1(2(5(1(0(1(5(0(2(1(2(4(5(3(1(4(4(1(2(1(2(2(1(1(5(4(5(0(1(0(3(3(3(5(0(0(1(5(4(4(5(0(1(3(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(1(3(0(1(0(2(3(0(3(2(5(4(2(3(4(4(2(2(1(2(5(0(5(4(2(1(2(2(0(5(5(2(3(4(3(3(5(2(3(1(0(5(1(3(2(4(0(3(0(3(0(2(0(4(3(5(5(0(2(3(3(4(5(3(4(5(0(4(5(2(3(1(0(5(0(0(2(3(1(2(0(4(3(3(4(3(4(4(4(0(5(2(3(4(1(5(2(5(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(2(1(5(5(0(5(5(3(2(3(3(0(0(4(0(4(1(2(4(0(4(3(2(4(5(4(0(2(2(3(5(3(2(5(0(0(3(2(4(0(1(5(2(3(2(1(2(5(0(2(0(4(1(3(1(1(2(2(0(1(3(1(4(5(3(3(4(4(4(0(0(5(4(1(3(3(5(1(0(4(1(3(3(3(4(0(4(5(3(3(4(1(4(4(4(3(3(5(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(0(4(0(0(2(4(1(2(2(1(5(5(4(2(3(3(1(5(0(2(0(2(4(2(2(1(2(3(5(3(3(4(4(4(2(1(2(1(3(2(0(3(4(3(0(1(4(0(5(1(0(2(5(2(3(2(2(3(3(3(2(0(0(3(3(5(3(1(5(4(5(4(5(0(2(5(5(5(1(1(3(5(4(3(1(2(5(1(4(0(1(0(3(5(3(2(2(3(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(4(5(5(3(2(3(3(3(1(5(3(5(2(3(5(0(0(4(1(5(4(2(3(5(5(0(1(5(4(4(0(1(3(4(3(0(0(3(5(5(5(0(3(2(3(0(2(2(5(1(2(2(4(3(2(3(4(2(4(5(2(2(1(3(1(4(5(3(2(2(2(5(2(4(5(0(2(4(4(3(3(1(4(4(2(3(0(3(4(3(4(0(3(3(3(0(3(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(3(0(3(1(0(0(3(2(2(3(1(0(1(4(3(5(4(1(3(2(2(0(1(1(2(0(4(0(4(0(0(1(3(0(0(0(4(4(4(5(0(3(0(1(1(3(5(4(2(3(4(5(5(0(2(3(5(0(2(3(2(3(4(5(0(5(1(0(2(0(2(1(0(5(0(1(1(2(4(0(1(1(1(5(3(1(2(1(1(4(3(0(1(0(2(0(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 1(5(1(3(1(2(0(5(4(3(4(2(3(4(5(3(4(2(3(5(1(5(1(1(3(2(2(4(4(3(3(2(1(4(1(1(1(4(3(4(0(1(5(1(4(1(1(2(3(3(4(4(5(5(0(2(5(4(5(3(3(2(3(5(1(4(2(3(2(5(2(3(3(1(4(4(3(4(3(5(1(3(3(1(0(0(2(2(1(2(4(0(4(3(4(2(5(3(5(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(0(3(3(2(0(3(2(3(1(1(0(2(3(4(0(4(5(2(3(3(5(2(3(5(0(1(2(1(4(2(0(4(4(0(0(5(0(2(5(3(0(3(2(1(2(2(2(3(2(3(0(3(3(0(5(5(3(2(3(3(1(0(3(0(4(0(0(4(0(5(3(1(3(3(3(5(5(1(4(1(5(1(5(1(5(5(3(4(3(1(2(1(2(2(4(5(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2(1(5(0(0(0(4(5(2(0(3(4(5(5(3(4(4(3(1(0(0(2(0(5(0(1(4(0(3(2(3(5(0(2(2(4(5(5(3(0(1(1(2(4(5(2(4(4(2(2(5(3(1(3(0(2(0(2(2(1(1(0(5(5(0(1(3(2(4(1(3(1(3(2(5(3(4(3(5(5(0(1(5(0(4(5(1(2(1(2(3(0(1(1(2(0(5(3(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(5(1(0(3(4(2(3(3(1(2(3(2(5(0(1(0(2(3(3(0(5(1(1(1(1(4(1(2(1(0(4(3(4(0(2(2(1(1(0(2(3(2(2(4(4(3(3(3(1(5(2(4(5(4(4(4(0(2(2(0(3(0(5(1(1(4(4(5(5(2(1(3(3(1(3(5(2(4(4(0(2(1(4(2(5(5(5(5(5(4(0(3(3(4(2(1(0(5(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2(1(5(2(5(1(1(5(5(5(0(5(5(1(2(3(1(2(1(2(2(3(4(3(3(2(4(2(5(5(1(3(0(5(5(5(0(3(4(0(1(5(1(2(4(2(3(2(4(1(4(3(1(4(3(3(1(2(2(5(4(2(2(0(0(5(3(5(4(2(4(2(1(1(1(2(4(2(1(3(0(4(4(0(0(4(3(5(0(3(2(5(4(4(5(3(3(3(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(5(5(3(3(0(0(3(0(5(0(0(4(3(5(3(3(1(4(0(1(4(2(5(1(2(1(0(2(4(4(3(2(2(0(3(1(4(4(0(2(4(4(2(3(2(2(5(4(3(5(0(1(0(3(1(4(2(1(0(0(5(0(4(5(5(1(4(4(5(0(3(2(2(1(0(1(4(2(3(4(1(0(1(1(2(3(3(2(1(3(2(1(3(2(5(1(5(1(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2(3(0(3(5(4(2(5(5(1(5(1(1(2(1(2(0(0(4(5(2(4(2(1(0(1(1(4(1(4(5(2(2(3(2(2(4(5(5(4(2(4(4(0(2(4(5(1(3(1(4(4(3(3(5(5(5(1(5(4(0(0(3(5(5(2(4(3(4(5(0(5(4(2(3(5(2(1(4(0(0(5(4(1(4(1(3(3(0(1(1(4(0(4(0(4(4(4(0(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(0(1(0(1(0(5(5(0(4(2(3(0(0(4(3(4(3(4(0(3(1(4(5(5(5(2(0(4(0(5(3(2(2(2(1(2(0(2(1(3(3(4(3(2(3(1(5(4(4(5(2(4(2(5(2(5(3(4(5(1(1(4(3(4(0(0(2(4(4(0(1(5(2(5(4(2(4(2(5(3(5(0(4(3(5(4(0(4(4(0(4(4(5(4(4(0(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(0(0(5(0(1(3(1(0(1(0(1(4(2(1(1(3(0(5(5(3(1(4(0(1(1(2(5(1(4(0(0(2(5(4(1(4(3(1(5(0(0(1(2(3(0(5(5(5(5(5(5(3(2(3(1(0(5(4(1(1(4(2(5(0(4(5(2(0(4(1(5(2(4(5(3(1(5(3(1(1(4(3(0(5(2(3(4(1(0(1(3(3(1(3(0(3(3(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(0(4(2(2(3(0(1(0(3(3(4(3(1(4(1(5(4(4(3(1(5(5(4(5(1(4(3(2(1(0(3(3(3(1(5(5(5(5(4(2(1(1(1(1(0(3(3(2(3(3(2(3(4(3(3(5(2(3(5(3(5(4(2(0(0(3(0(0(0(5(0(4(1(4(0(1(4(2(1(5(4(0(5(4(4(0(2(5(4(0(4(5(1(2(0(3(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(3(1(5(5(4(4(2(2(4(1(0(4(4(5(1(3(0(1(0(0(3(3(2(4(0(0(3(3(4(3(3(2(0(1(2(5(2(0(2(2(1(1(5(3(4(0(2(0(1(3(2(1(1(4(5(1(2(1(5(0(3(4(5(1(2(5(3(3(0(1(5(2(4(5(2(0(2(2(4(2(1(4(4(1(5(4(2(2(0(4(2(1(0(4(0(3(3(2(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(1(1(0(3(3(5(2(5(5(3(4(1(3(4(5(3(5(2(3(4(3(5(1(3(0(4(3(3(1(0(1(0(1(1(1(4(3(5(2(5(1(2(1(4(3(0(0(5(4(0(1(2(1(3(3(1(2(4(3(2(3(1(5(1(2(4(3(1(3(5(3(1(0(4(4(3(1(2(0(4(5(2(1(1(2(4(1(0(2(0(0(1(4(1(2(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(4(0(2(5(5(5(0(1(5(2(2(2(3(3(3(5(1(4(4(2(3(3(2(4(1(2(0(0(4(5(1(3(1(0(5(1(0(1(4(1(3(4(2(2(2(0(5(3(1(3(0(0(5(4(4(5(0(4(2(5(2(2(2(2(4(5(4(1(0(0(4(5(4(4(1(1(5(2(1(3(3(0(5(0(3(1(4(4(4(2(4(5(2(5(1(5(3(5(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(0(2(2(4(3(4(4(1(5(1(5(5(3(4(2(1(2(2(2(3(3(2(1(1(1(5(0(5(3(0(2(5(4(0(2(5(3(1(0(2(1(3(1(1(3(4(3(3(0(0(4(4(1(2(2(4(2(1(2(4(1(3(4(1(3(5(1(3(2(0(5(1(0(4(1(2(0(5(1(4(1(5(2(3(3(5(0(5(3(2(4(1(5(0(3(3(1(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(4(2(5(2(5(3(0(1(5(2(1(0(2(5(5(2(3(0(4(3(5(3(2(3(0(2(1(5(5(0(1(4(2(1(5(5(5(0(2(3(3(5(4(2(1(5(3(5(5(4(1(3(3(0(0(2(5(0(1(3(3(3(0(2(2(0(1(4(4(4(5(1(5(3(4(3(3(0(2(4(4(0(3(5(0(4(2(4(3(5(0(0(5(4(2(2(1(5(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(4(4(3(1(1(3(1(4(1(1(0(0(0(1(2(0(3(3(4(3(0(5(5(5(4(2(4(3(4(0(5(1(3(3(4(0(3(5(5(0(5(4(3(2(1(0(3(1(0(0(0(5(2(3(4(4(3(0(2(3(1(0(0(1(5(2(3(3(3(4(5(5(3(5(2(0(5(4(1(4(5(2(3(5(4(4(5(1(4(2(4(1(1(5(1(1(3(5(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(5(3(4(1(4(4(2(5(5(0(1(4(2(1(4(1(3(5(2(2(0(5(0(0(0(0(2(3(0(0(0(3(5(2(1(5(5(4(4(0(0(4(2(1(1(0(2(0(5(2(2(0(5(1(1(3(0(5(5(2(0(1(4(2(4(4(3(3(4(5(2(3(5(5(4(2(2(4(5(3(5(5(2(5(3(2(1(3(5(2(2(5(3(2(1(3(0(4(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(3(4(0(3(5(4(3(5(4(5(1(4(4(2(3(2(4(3(0(0(2(5(5(2(5(1(3(3(1(2(4(5(0(0(3(1(2(5(3(1(3(4(1(1(3(5(4(4(3(1(5(3(3(1(0(3(1(3(1(4(4(0(4(2(1(2(2(5(3(2(3(4(5(5(0(1(0(0(3(2(4(0(2(4(1(5(5(3(1(1(5(5(0(3(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 4(4(1(4(4(1(4(4(4(2(0(3(1(1(2(5(5(3(4(2(0(2(4(3(1(4(0(2(4(1(0(5(4(3(3(1(1(1(3(3(0(5(4(4(0(5(3(2(4(0(2(2(5(0(3(0(2(1(3(2(3(0(2(1(4(1(3(0(2(4(5(0(4(1(2(3(0(4(1(1(5(4(5(4(4(0(5(0(2(4(1(5(3(0(5(5(5(0(2(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(2(0(3(0(2(1(1(0(2(4(4(2(2(3(2(4(3(0(1(1(0(2(2(4(0(2(2(4(3(2(3(0(3(2(4(5(5(2(4(3(3(5(1(4(2(0(3(3(4(4(5(2(3(2(0(4(5(1(4(4(5(4(3(5(2(0(4(2(4(2(0(2(4(2(2(0(0(4(5(4(3(1(4(3(0(0(1(3(4(5(1(5(0(0(1(2(5(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 4(4(2(4(5(4(2(4(3(1(5(5(4(4(0(2(1(0(5(4(3(3(1(5(5(3(5(4(5(1(1(3(1(3(1(2(5(5(1(1(4(4(3(1(4(3(1(5(0(3(5(4(1(4(0(2(2(1(1(5(4(5(3(5(3(1(5(2(2(2(5(3(4(1(0(4(0(1(4(2(5(5(5(0(3(0(2(0(0(5(4(2(1(0(3(1(5(4(5(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(0(0(5(3(5(5(1(4(3(1(5(1(3(1(2(2(1(5(1(4(0(5(5(4(5(5(5(0(4(0(2(0(1(5(2(5(1(1(0(5(4(5(5(5(2(4(3(2(0(4(1(2(1(5(1(0(0(1(1(2(1(0(4(1(3(1(3(5(4(2(0(4(0(5(2(5(3(5(5(1(0(5(5(0(2(0(2(3(3(2(1(1(3(5(5(2(2(2(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(0(5(1(2(2(5(5(1(4(3(4(5(1(5(4(3(4(5(2(3(1(4(2(3(0(1(5(0(0(1(1(0(3(1(1(5(5(4(1(5(0(5(0(0(5(3(3(2(3(3(5(4(1(3(3(3(3(1(4(1(3(2(5(4(2(0(4(5(3(0(0(3(3(3(5(1(4(3(1(1(4(1(5(5(4(2(1(3(5(5(4(4(1(3(3(1(1(0(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(5(4(0(2(5(5(1(4(1(2(0(1(4(0(4(2(2(2(5(0(2(2(0(3(0(4(4(5(0(2(2(0(2(0(3(4(3(5(3(2(2(0(1(5(3(1(2(5(3(5(2(1(2(3(5(0(1(0(4(1(3(1(3(5(0(5(3(4(3(0(2(0(0(2(4(5(5(2(0(2(4(2(3(5(5(3(0(2(2(3(2(3(5(3(1(1(1(5(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(1(3(3(0(5(1(4(1(2(2(4(1(1(0(5(4(2(0(5(2(3(4(4(3(5(2(1(1(5(5(4(4(1(2(2(5(2(5(3(4(2(1(0(4(4(1(0(3(0(2(5(3(2(5(0(0(2(1(4(3(1(0(3(5(4(0(5(4(5(0(4(0(3(2(4(3(5(3(0(2(2(1(2(3(5(1(3(4(5(5(0(4(2(4(2(4(5(5(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(2(1(3(0(0(2(0(0(3(1(2(3(2(0(4(0(1(0(2(3(4(1(5(3(4(5(1(1(3(4(2(0(4(2(1(2(3(2(1(0(1(4(4(3(5(0(0(3(2(5(3(3(3(2(3(4(2(1(4(5(5(5(4(3(5(3(5(3(4(5(0(0(4(2(5(1(5(5(2(3(3(0(2(5(3(1(4(5(0(0(0(1(1(3(1(2(5(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(1(5(5(2(1(5(4(0(3(2(5(2(3(0(4(2(3(2(0(3(4(1(1(5(3(3(0(4(3(4(5(4(2(2(4(1(0(3(1(0(2(4(4(3(1(0(2(3(1(1(4(4(4(0(0(4(2(4(0(1(3(4(5(1(3(3(5(4(0(5(4(2(3(3(1(4(5(0(4(5(0(5(3(4(0(0(0(2(3(4(4(1(4(5(1(4(0(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(2(3(4(5(2(4(0(5(5(0(3(1(2(4(2(5(5(1(2(4(5(1(4(1(5(4(5(2(2(5(3(1(3(2(0(1(0(1(5(4(4(0(5(5(4(1(3(5(2(3(4(0(4(3(2(0(5(0(3(0(4(5(0(4(4(3(1(2(3(5(2(5(2(1(0(2(0(0(1(3(5(1(4(3(3(2(2(0(3(3(1(0(4(4(4(2(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(5(2(5(0(3(3(5(1(1(1(1(4(4(0(5(1(0(1(5(2(4(2(4(3(2(5(3(3(5(1(0(0(3(0(4(1(3(0(2(5(2(3(1(5(0(2(0(1(5(5(4(0(5(3(1(0(2(1(2(3(3(1(4(5(5(5(2(3(5(3(5(2(1(2(5(3(3(0(3(3(3(4(0(3(3(4(4(5(3(3(0(0(3(5(3(3(1(5(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(1(1(3(2(4(5(2(0(3(0(1(4(5(0(4(2(0(2(3(1(3(4(0(2(3(4(1(0(4(4(1(0(5(2(0(3(0(5(5(4(3(3(2(2(5(1(2(1(1(5(2(5(0(4(2(1(0(0(5(3(0(0(4(5(2(0(2(0(2(2(2(1(4(0(1(1(5(1(1(2(1(0(3(1(3(1(3(3(3(0(1(2(5(2(3(4(1(1(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(5(4(5(0(3(5(3(0(4(1(5(2(2(5(1(5(1(1(4(2(0(3(1(3(4(0(1(5(2(4(5(5(0(5(0(5(5(4(5(3(1(4(3(3(3(1(1(5(0(0(4(5(5(2(3(4(4(1(3(4(0(0(1(5(3(1(3(1(5(5(1(2(5(1(2(4(3(3(5(4(1(1(2(4(2(1(4(4(1(0(0(4(5(4(3(2(5(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(1(5(3(1(0(3(2(2(2(4(5(5(3(2(4(3(0(2(2(5(2(3(0(2(2(2(4(1(2(0(3(5(5(1(3(4(4(2(1(1(4(1(1(0(1(5(5(1(1(1(5(2(2(4(4(1(4(2(2(1(1(3(1(2(2(2(3(1(1(4(5(5(3(4(0(5(4(0(5(3(2(0(0(1(4(4(5(1(1(4(2(1(1(2(0(5(4(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(0(1(2(3(1(4(4(1(0(5(4(4(2(3(5(5(3(2(3(4(0(4(0(4(3(5(4(2(4(0(1(4(2(1(1(2(4(4(4(0(2(5(1(3(0(0(0(2(4(3(2(1(4(1(4(5(2(4(0(2(5(1(2(3(3(4(5(0(0(0(1(1(0(0(4(3(4(4(3(0(3(5(0(4(3(2(5(2(3(2(4(1(4(5(5(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(2(3(5(1(0(3(1(0(5(1(5(1(5(2(2(2(1(4(1(4(1(3(0(1(0(4(0(3(3(4(5(5(5(1(5(4(3(5(1(4(0(5(5(3(3(3(4(4(0(5(2(3(5(1(3(2(3(4(5(4(2(5(4(0(0(3(2(3(4(4(0(4(2(0(1(3(3(5(2(2(4(0(1(4(3(2(4(1(4(0(1(3(1(3(4(3(2(0(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(2(3(1(5(1(5(5(2(0(0(0(3(0(2(2(5(5(5(0(1(0(1(3(3(1(4(4(1(2(3(5(1(3(2(1(2(2(4(5(1(3(4(1(0(3(1(2(4(2(4(1(1(4(1(2(5(1(0(1(5(0(2(1(2(4(5(3(1(4(4(1(2(1(2(2(1(1(5(4(5(0(1(0(3(3(3(5(0(0(1(5(4(4(5(0(1(3(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(1(3(0(1(0(2(3(0(3(2(5(4(2(3(4(4(2(2(1(2(5(0(5(4(2(1(2(2(0(5(5(2(3(4(3(3(5(2(3(1(0(5(1(3(2(4(0(3(0(3(0(2(0(4(3(5(5(0(2(3(3(4(5(3(4(5(0(4(5(2(3(1(0(5(0(0(2(3(1(2(0(4(3(3(4(3(4(4(4(0(5(2(3(4(1(5(2(5(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(2(1(5(5(0(5(5(3(2(3(3(0(0(4(0(4(1(2(4(0(4(3(2(4(5(4(0(2(2(3(5(3(2(5(0(0(3(2(4(0(1(5(2(3(2(1(2(5(0(2(0(4(1(3(1(1(2(2(0(1(3(1(4(5(3(3(4(4(4(0(0(5(4(1(3(3(5(1(0(4(1(3(3(3(4(0(4(5(3(3(4(1(4(4(4(3(3(5(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(0(4(0(0(2(4(1(2(2(1(5(5(4(2(3(3(1(5(0(2(0(2(4(2(2(1(2(3(5(3(3(4(4(4(2(1(2(1(3(2(0(3(4(3(0(1(4(0(5(1(0(2(5(2(3(2(2(3(3(3(2(0(0(3(3(5(3(1(5(4(5(4(5(0(2(5(5(5(1(1(3(5(4(3(1(2(5(1(4(0(1(0(3(5(3(2(2(3(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(4(5(5(3(2(3(3(3(1(5(3(5(2(3(5(0(0(4(1(5(4(2(3(5(5(0(1(5(4(4(0(1(3(4(3(0(0(3(5(5(5(0(3(2(3(0(2(2(5(1(2(2(4(3(2(3(4(2(4(5(2(2(1(3(1(4(5(3(2(2(2(5(2(4(5(0(2(4(4(3(3(1(4(4(2(3(0(3(4(3(4(0(3(3(3(0(3(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(3(0(3(1(0(0(3(2(2(3(1(0(1(4(3(5(4(1(3(2(2(0(1(1(2(0(4(0(4(0(0(1(3(0(0(0(4(4(4(5(0(3(0(1(1(3(5(4(2(3(4(5(5(0(2(3(5(0(2(3(2(3(4(5(0(5(1(0(2(0(2(1(0(5(0(1(1(2(4(0(1(1(1(5(3(1(2(1(1(4(3(0(1(0(2(0(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 1(5(1(3(1(2(0(5(4(3(4(2(3(4(5(3(4(2(3(5(1(5(1(1(3(2(2(4(4(3(3(2(1(4(1(1(1(4(3(4(0(1(5(1(4(1(1(2(3(3(4(4(5(5(0(2(5(4(5(3(3(2(3(5(1(4(2(3(2(5(2(3(3(1(4(4(3(4(3(5(1(3(3(1(0(0(2(2(1(2(4(0(4(3(4(2(5(3(5(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(0(3(3(2(0(3(2(3(1(1(0(2(3(4(0(4(5(2(3(3(5(2(3(5(0(1(2(1(4(2(0(4(4(0(0(5(0(2(5(3(0(3(2(1(2(2(2(3(2(3(0(3(3(0(5(5(3(2(3(3(1(0(3(0(4(0(0(4(0(5(3(1(3(3(3(5(5(1(4(1(5(1(5(1(5(5(3(4(3(1(2(1(2(2(4(5(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2(1(5(0(0(0(4(5(2(0(3(4(5(5(3(4(4(3(1(0(0(2(0(5(0(1(4(0(3(2(3(5(0(2(2(4(5(5(3(0(1(1(2(4(5(2(4(4(2(2(5(3(1(3(0(2(0(2(2(1(1(0(5(5(0(1(3(2(4(1(3(1(3(2(5(3(4(3(5(5(0(1(5(0(4(5(1(2(1(2(3(0(1(1(2(0(5(3(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(5(1(0(3(4(2(3(3(1(2(3(2(5(0(1(0(2(3(3(0(5(1(1(1(1(4(1(2(1(0(4(3(4(0(2(2(1(1(0(2(3(2(2(4(4(3(3(3(1(5(2(4(5(4(4(4(0(2(2(0(3(0(5(1(1(4(4(5(5(2(1(3(3(1(3(5(2(4(4(0(2(1(4(2(5(5(5(5(5(4(0(3(3(4(2(1(0(5(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2(1(5(2(5(1(1(5(5(5(0(5(5(1(2(3(1(2(1(2(2(3(4(3(3(2(4(2(5(5(1(3(0(5(5(5(0(3(4(0(1(5(1(2(4(2(3(2(4(1(4(3(1(4(3(3(1(2(2(5(4(2(2(0(0(5(3(5(4(2(4(2(1(1(1(2(4(2(1(3(0(4(4(0(0(4(3(5(0(3(2(5(4(4(5(3(3(3(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(5(5(3(3(0(0(3(0(5(0(0(4(3(5(3(3(1(4(0(1(4(2(5(1(2(1(0(2(4(4(3(2(2(0(3(1(4(4(0(2(4(4(2(3(2(2(5(4(3(5(0(1(0(3(1(4(2(1(0(0(5(0(4(5(5(1(4(4(5(0(3(2(2(1(0(1(4(2(3(4(1(0(1(1(2(3(3(2(1(3(2(1(3(2(5(1(5(1(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2(3(0(3(5(4(2(5(5(1(5(1(1(2(1(2(0(0(4(5(2(4(2(1(0(1(1(4(1(4(5(2(2(3(2(2(4(5(5(4(2(4(4(0(2(4(5(1(3(1(4(4(3(3(5(5(5(1(5(4(0(0(3(5(5(2(4(3(4(5(0(5(4(2(3(5(2(1(4(0(0(5(4(1(4(1(3(3(0(1(1(4(0(4(0(4(4(4(0(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(0(1(0(1(0(5(5(0(4(2(3(0(0(4(3(4(3(4(0(3(1(4(5(5(5(2(0(4(0(5(3(2(2(2(1(2(0(2(1(3(3(4(3(2(3(1(5(4(4(5(2(4(2(5(2(5(3(4(5(1(1(4(3(4(0(0(2(4(4(0(1(5(2(5(4(2(4(2(5(3(5(0(4(3(5(4(0(4(4(0(4(4(5(4(4(0(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(0(0(5(0(1(3(1(0(1(0(1(4(2(1(1(3(0(5(5(3(1(4(0(1(1(2(5(1(4(0(0(2(5(4(1(4(3(1(5(0(0(1(2(3(0(5(5(5(5(5(5(3(2(3(1(0(5(4(1(1(4(2(5(0(4(5(2(0(4(1(5(2(4(5(3(1(5(3(1(1(4(3(0(5(2(3(4(1(0(1(3(3(1(3(0(3(3(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(0(4(2(2(3(0(1(0(3(3(4(3(1(4(1(5(4(4(3(1(5(5(4(5(1(4(3(2(1(0(3(3(3(1(5(5(5(5(4(2(1(1(1(1(0(3(3(2(3(3(2(3(4(3(3(5(2(3(5(3(5(4(2(0(0(3(0(0(0(5(0(4(1(4(0(1(4(2(1(5(4(0(5(4(4(0(2(5(4(0(4(5(1(2(0(3(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(3(1(5(5(4(4(2(2(4(1(0(4(4(5(1(3(0(1(0(0(3(3(2(4(0(0(3(3(4(3(3(2(0(1(2(5(2(0(2(2(1(1(5(3(4(0(2(0(1(3(2(1(1(4(5(1(2(1(5(0(3(4(5(1(2(5(3(3(0(1(5(2(4(5(2(0(2(2(4(2(1(4(4(1(5(4(2(2(0(4(2(1(0(4(0(3(3(2(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(1(1(0(3(3(5(2(5(5(3(4(1(3(4(5(3(5(2(3(4(3(5(1(3(0(4(3(3(1(0(1(0(1(1(1(4(3(5(2(5(1(2(1(4(3(0(0(5(4(0(1(2(1(3(3(1(2(4(3(2(3(1(5(1(2(4(3(1(3(5(3(1(0(4(4(3(1(2(0(4(5(2(1(1(2(4(1(0(2(0(0(1(4(1(2(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(4(0(2(5(5(5(0(1(5(2(2(2(3(3(3(5(1(4(4(2(3(3(2(4(1(2(0(0(4(5(1(3(1(0(5(1(0(1(4(1(3(4(2(2(2(0(5(3(1(3(0(0(5(4(4(5(0(4(2(5(2(2(2(2(4(5(4(1(0(0(4(5(4(4(1(1(5(2(1(3(3(0(5(0(3(1(4(4(4(2(4(5(2(5(1(5(3(5(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(0(2(2(4(3(4(4(1(5(1(5(5(3(4(2(1(2(2(2(3(3(2(1(1(1(5(0(5(3(0(2(5(4(0(2(5(3(1(0(2(1(3(1(1(3(4(3(3(0(0(4(4(1(2(2(4(2(1(2(4(1(3(4(1(3(5(1(3(2(0(5(1(0(4(1(2(0(5(1(4(1(5(2(3(3(5(0(5(3(2(4(1(5(0(3(3(1(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(4(2(5(2(5(3(0(1(5(2(1(0(2(5(5(2(3(0(4(3(5(3(2(3(0(2(1(5(5(0(1(4(2(1(5(5(5(0(2(3(3(5(4(2(1(5(3(5(5(4(1(3(3(0(0(2(5(0(1(3(3(3(0(2(2(0(1(4(4(4(5(1(5(3(4(3(3(0(2(4(4(0(3(5(0(4(2(4(3(5(0(0(5(4(2(2(1(5(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(4(4(3(1(1(3(1(4(1(1(0(0(0(1(2(0(3(3(4(3(0(5(5(5(4(2(4(3(4(0(5(1(3(3(4(0(3(5(5(0(5(4(3(2(1(0(3(1(0(0(0(5(2(3(4(4(3(0(2(3(1(0(0(1(5(2(3(3(3(4(5(5(3(5(2(0(5(4(1(4(5(2(3(5(4(4(5(1(4(2(4(1(1(5(1(1(3(5(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(5(3(4(1(4(4(2(5(5(0(1(4(2(1(4(1(3(5(2(2(0(5(0(0(0(0(2(3(0(0(0(3(5(2(1(5(5(4(4(0(0(4(2(1(1(0(2(0(5(2(2(0(5(1(1(3(0(5(5(2(0(1(4(2(4(4(3(3(4(5(2(3(5(5(4(2(2(4(5(3(5(5(2(5(3(2(1(3(5(2(2(5(3(2(1(3(0(4(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(3(4(0(3(5(4(3(5(4(5(1(4(4(2(3(2(4(3(0(0(2(5(5(2(5(1(3(3(1(2(4(5(0(0(3(1(2(5(3(1(3(4(1(1(3(5(4(4(3(1(5(3(3(1(0(3(1(3(1(4(4(0(4(2(1(2(2(5(3(2(3(4(5(5(0(1(0(0(3(2(4(0(2(4(1(5(5(3(1(1(5(5(0(3(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 4(4(1(4(4(1(4(4(4(2(0(3(1(1(2(5(5(3(4(2(0(2(4(3(1(4(0(2(4(1(0(5(4(3(3(1(1(1(3(3(0(5(4(4(0(5(3(2(4(0(2(2(5(0(3(0(2(1(3(2(3(0(2(1(4(1(3(0(2(4(5(0(4(1(2(3(0(4(1(1(5(4(5(4(4(0(5(0(2(4(1(5(3(0(5(5(5(0(2(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(2(0(3(0(2(1(1(0(2(4(4(2(2(3(2(4(3(0(1(1(0(2(2(4(0(2(2(4(3(2(3(0(3(2(4(5(5(2(4(3(3(5(1(4(2(0(3(3(4(4(5(2(3(2(0(4(5(1(4(4(5(4(3(5(2(0(4(2(4(2(0(2(4(2(2(0(0(4(5(4(3(1(4(3(0(0(1(3(4(5(1(5(0(0(1(2(5(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 4(4(2(4(5(4(2(4(3(1(5(5(4(4(0(2(1(0(5(4(3(3(1(5(5(3(5(4(5(1(1(3(1(3(1(2(5(5(1(1(4(4(3(1(4(3(1(5(0(3(5(4(1(4(0(2(2(1(1(5(4(5(3(5(3(1(5(2(2(2(5(3(4(1(0(4(0(1(4(2(5(5(5(0(3(0(2(0(0(5(4(2(1(0(3(1(5(4(5(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(0(0(5(3(5(5(1(4(3(1(5(1(3(1(2(2(1(5(1(4(0(5(5(4(5(5(5(0(4(0(2(0(1(5(2(5(1(1(0(5(4(5(5(5(2(4(3(2(0(4(1(2(1(5(1(0(0(1(1(2(1(0(4(1(3(1(3(5(4(2(0(4(0(5(2(5(3(5(5(1(0(5(5(0(2(0(2(3(3(2(1(1(3(5(5(2(2(2(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(0(5(1(2(2(5(5(1(4(3(4(5(1(5(4(3(4(5(2(3(1(4(2(3(0(1(5(0(0(1(1(0(3(1(1(5(5(4(1(5(0(5(0(0(5(3(3(2(3(3(5(4(1(3(3(3(3(1(4(1(3(2(5(4(2(0(4(5(3(0(0(3(3(3(5(1(4(3(1(1(4(1(5(5(4(2(1(3(5(5(4(4(1(3(3(1(1(0(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(5(4(0(2(5(5(1(4(1(2(0(1(4(0(4(2(2(2(5(0(2(2(0(3(0(4(4(5(0(2(2(0(2(0(3(4(3(5(3(2(2(0(1(5(3(1(2(5(3(5(2(1(2(3(5(0(1(0(4(1(3(1(3(5(0(5(3(4(3(0(2(0(0(2(4(5(5(2(0(2(4(2(3(5(5(3(0(2(2(3(2(3(5(3(1(1(1(5(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(1(3(3(0(5(1(4(1(2(2(4(1(1(0(5(4(2(0(5(2(3(4(4(3(5(2(1(1(5(5(4(4(1(2(2(5(2(5(3(4(2(1(0(4(4(1(0(3(0(2(5(3(2(5(0(0(2(1(4(3(1(0(3(5(4(0(5(4(5(0(4(0(3(2(4(3(5(3(0(2(2(1(2(3(5(1(3(4(5(5(0(4(2(4(2(4(5(5(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(2(1(3(0(0(2(0(0(3(1(2(3(2(0(4(0(1(0(2(3(4(1(5(3(4(5(1(1(3(4(2(0(4(2(1(2(3(2(1(0(1(4(4(3(5(0(0(3(2(5(3(3(3(2(3(4(2(1(4(5(5(5(4(3(5(3(5(3(4(5(0(0(4(2(5(1(5(5(2(3(3(0(2(5(3(1(4(5(0(0(0(1(1(3(1(2(5(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(1(5(5(2(1(5(4(0(3(2(5(2(3(0(4(2(3(2(0(3(4(1(1(5(3(3(0(4(3(4(5(4(2(2(4(1(0(3(1(0(2(4(4(3(1(0(2(3(1(1(4(4(4(0(0(4(2(4(0(1(3(4(5(1(3(3(5(4(0(5(4(2(3(3(1(4(5(0(4(5(0(5(3(4(0(0(0(2(3(4(4(1(4(5(1(4(0(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(2(3(4(5(2(4(0(5(5(0(3(1(2(4(2(5(5(1(2(4(5(1(4(1(5(4(5(2(2(5(3(1(3(2(0(1(0(1(5(4(4(0(5(5(4(1(3(5(2(3(4(0(4(3(2(0(5(0(3(0(4(5(0(4(4(3(1(2(3(5(2(5(2(1(0(2(0(0(1(3(5(1(4(3(3(2(2(0(3(3(1(0(4(4(4(2(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(5(2(5(0(3(3(5(1(1(1(1(4(4(0(5(1(0(1(5(2(4(2(4(3(2(5(3(3(5(1(0(0(3(0(4(1(3(0(2(5(2(3(1(5(0(2(0(1(5(5(4(0(5(3(1(0(2(1(2(3(3(1(4(5(5(5(2(3(5(3(5(2(1(2(5(3(3(0(3(3(3(4(0(3(3(4(4(5(3(3(0(0(3(5(3(3(1(5(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(1(1(3(2(4(5(2(0(3(0(1(4(5(0(4(2(0(2(3(1(3(4(0(2(3(4(1(0(4(4(1(0(5(2(0(3(0(5(5(4(3(3(2(2(5(1(2(1(1(5(2(5(0(4(2(1(0(0(5(3(0(0(4(5(2(0(2(0(2(2(2(1(4(0(1(1(5(1(1(2(1(0(3(1(3(1(3(3(3(0(1(2(5(2(3(4(1(1(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(5(4(5(0(3(5(3(0(4(1(5(2(2(5(1(5(1(1(4(2(0(3(1(3(4(0(1(5(2(4(5(5(0(5(0(5(5(4(5(3(1(4(3(3(3(1(1(5(0(0(4(5(5(2(3(4(4(1(3(4(0(0(1(5(3(1(3(1(5(5(1(2(5(1(2(4(3(3(5(4(1(1(2(4(2(1(4(4(1(0(0(4(5(4(3(2(5(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(1(5(3(1(0(3(2(2(2(4(5(5(3(2(4(3(0(2(2(5(2(3(0(2(2(2(4(1(2(0(3(5(5(1(3(4(4(2(1(1(4(1(1(0(1(5(5(1(1(1(5(2(2(4(4(1(4(2(2(1(1(3(1(2(2(2(3(1(1(4(5(5(3(4(0(5(4(0(5(3(2(0(0(1(4(4(5(1(1(4(2(1(1(2(0(5(4(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules:
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Derivational Complexity: TRS