0.00/0.55
0.00/0.55
(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
g(x, y) → x
0.00/0.55
g(x, y) → y
0.00/0.55
f(s(x), y, y) → f(y, x, s(x))
Rewrite Strategy: INNERMOST
0.00/0.55
0.00/0.55
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
0.00/0.55
0.00/0.55
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
g(z0, z1) → z0
0.00/0.55
g(z0, z1) → z1
0.00/0.55
f(s(z0), z1, z1) → f(z1, z0, s(z0))
Tuples:
F(s(z0), z1, z1) → c2(F(z1, z0, s(z0)))
S tuples:
F(s(z0), z1, z1) → c2(F(z1, z0, s(z0)))
K tuples:none
Defined Rule Symbols:
g, f
Defined Pair Symbols:
F
Compound Symbols:
c2
0.00/0.55
0.00/0.55
(3) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing tuple parts
0.00/0.55
0.00/0.55
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
g(z0, z1) → z0
0.00/0.55
g(z0, z1) → z1
0.00/0.55
f(s(z0), z1, z1) → f(z1, z0, s(z0))
Tuples:
F(s(z0), z1, z1) → c2
S tuples:
F(s(z0), z1, z1) → c2
K tuples:none
Defined Rule Symbols:
g, f
Defined Pair Symbols:
F
Compound Symbols:
c2
0.00/0.55
0.00/0.55
(5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
F(s(z0), z1, z1) → c2
0.00/0.55
0.00/0.55
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
g(z0, z1) → z0
0.00/0.55
g(z0, z1) → z1
0.00/0.55
f(s(z0), z1, z1) → f(z1, z0, s(z0))
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
g, f
Defined Pair Symbols:none
Compound Symbols:none
0.00/0.55
0.00/0.55
(7) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
0.00/0.55
0.00/0.55
(8) BOUNDS(O(1), O(1))
0.00/0.55